Mathematics › Permutation & Combination
Permutation & Combination Questions
296 questions across 9 subtopics — with step-by-step solutions.
Arrangement under Constraint(53)
- How many ways are there to arrange the let... | Mathematics | TestHub
- How many different words can be formed by... | Mathematics | TestHub
- Consider all possible permutations of the... | Mathematics | TestHub
- Paragraph:Let be the set of all symmetric... | Mathematics | TestHub
- The number of seven digit integers, with s... | Mathematics | TestHub
- Let denote the number of all -digit positi... | Mathematics | TestHub
- Let denote the number of all -digit positi... | Mathematics | TestHub
- The number of ways in which an examiner ca... | Mathematics | TestHub
- A committee of 4 persons is to be formed f... | Mathematics | TestHub
- Letbe positive integers such that. Then th... | Mathematics | TestHub
- Three boys and two girls stand in a queue.... | Mathematics | TestHub
- Let n be the number of ways in which 5 boy... | Mathematics | TestHub
- Words of lengthare formed using the letter... | Mathematics | TestHub
- Fromdifferent novels anddifferent dictiona... | Mathematics | TestHub
- The number ofdigit numbers which are divis... | Mathematics | TestHub
- Consider a class ofgirls andboys. The numb... | Mathematics | TestHub
- Five personsandare seated in a circular ar... | Mathematics | TestHub
- The number of four-digit numbers strictly... | Mathematics | TestHub
- The number of words (with or without meani... | Mathematics | TestHub
- An engineer is required to visit a factory... | Mathematics | TestHub
- Total number ofdigit numbers in which only... | Mathematics | TestHub
- Two families with three members each and o... | Mathematics | TestHub
- The number of six letter words (with or wi... | Mathematics | TestHub
- If the digits are not allowed to repeat in... | Mathematics | TestHub
- The number of seven digit integers with su... | Mathematics | TestHub
- The number of times the digitwill be writt... | Mathematics | TestHub
- There arestudents in classstudents in clas... | Mathematics | TestHub
- The total number of numbers, lying between... | Mathematics | TestHub
- The number of-digit integers in the closed... | Mathematics | TestHub
- Let be a -element permutation with for and... | Mathematics | TestHub
- The total number of-digit numbers, formed... | Mathematics | TestHub
- Letbe the set of all passwords which are s... | Mathematics | TestHub
- Number of-digit numbers (the repetition of... | Mathematics | TestHub
- The number of permutations, of the digitsw... | Mathematics | TestHub
- The number of arrangements of the letters... | Mathematics | TestHub
- The number of five-digit numbers, greater... | Mathematics | TestHub
- The number of seven digits odd numbers, th... | Mathematics | TestHub
- Let the digitsbe in A.P. Nine-digit number... | Mathematics | TestHub
- The number of words, with or without meani... | Mathematics | TestHub
- The number ofdigit numbers, that can be fo... | Mathematics | TestHub
- Letbe the set of all five digit numbers fo... | Mathematics | TestHub
- If the number of words, with or without me... | Mathematics | TestHub
- 60 words can be made using all the letters... | Mathematics | TestHub
- All the letters of the wordare written in... | Mathematics | TestHub
- A group of 9 students, , is to be divided... | Mathematics | TestHub
- The number of words, which can be formed u... | Mathematics | TestHub
- In a group of 3 girls and 4 boys, there ar... | Mathematics | TestHub
- The number of ways, 5 boys and 4 girls can... | Mathematics | TestHub
- From all the English alphabets, five lette... | Mathematics | TestHub
- The number of ways of arranging 11 objects... | Mathematics | TestHub
- The number of onto functions which are non... | Mathematics | TestHub
- There are 6 balls of each of the four colo... | Mathematics | TestHub
- The number of ways of arranging the letter... | Mathematics | TestHub
Circular Permutation(3)
Dearrangement(3)
Distribution(6)
- Total number of ways in which 256 identica... | Mathematics | TestHub
- If \left\lfloor 15=2^{\mathrm{p}_{1}} 3^{\... | Mathematics | TestHub
- The number of ways of distributing 3 ident... | Mathematics | TestHub
- Out of 5 apples, 10 mangoes and 15 oranges... | Mathematics | TestHub
- Let there be 4 mangoes of which 2 are alik... | Mathematics | TestHub
- Five balls of different colours are to be... | Mathematics | TestHub
Division of Identical items(16)
- The total number ofdigit numbers whose sum... | Mathematics | TestHub
- The total number of positive integral solu... | Mathematics | TestHub
- In an examination, there aremultiple choic... | Mathematics | TestHub
- The number of ways,identical cubes, of whi... | Mathematics | TestHub
- The number of-digit odd numbers, whose sum... | Mathematics | TestHub
- The number of ways to distributeidentical... | Mathematics | TestHub
- Suppose Anil's mother wants to givewhole f... | Mathematics | TestHub
- The number of ways of giving distinct oran... | Mathematics | TestHub
- The number of tripletswhereare distinct no... | Mathematics | TestHub
- Number of integral solutions to the equati... | Mathematics | TestHub
- The number of seven digit positive integer... | Mathematics | TestHub
- Number of ways of arrangingidentical books... | Mathematics | TestHub
- The number of ways of getting a sum 16 on... | Mathematics | TestHub
- The number of ways in which identical appl... | Mathematics | TestHub
- For , let denote the set of all subsets of... | Mathematics | TestHub
- The no.of positive integer solutions of x+... | Mathematics | TestHub
Fundamental Principle(27)
- From a group of 7 batsmen and 6 bowlers, 1... | Mathematics | TestHub
- The number of different 5 digit numbers gr... | Mathematics | TestHub
- Line of slope 2 and line of slope intersec... | Mathematics | TestHub
- In a group of 3 girls and 4 boys, there ar... | Mathematics | TestHub
- There are 12 points in a plane, no three o... | Mathematics | TestHub
- The largest such that divides 50 ! is: | Mathematics | TestHub
- The number of ways, in which the letters ,... | Mathematics | TestHub
- The number of words, which can be formed u... | Mathematics | TestHub
- The number of sequences of ten terms, whos... | Mathematics | TestHub
- If all the words with or without meaning m... | Mathematics | TestHub
- Five digit numbers are formed by using the... | Mathematics | TestHub
- The number of 4 -digit numbers that can be... | Mathematics | TestHub
- Nine hundred distinct n -digit number s ar... | Mathematics | TestHub
- The number of polynomials of the form x^{3... | Mathematics | TestHub
- If a and b are positive integers and \math... | Mathematics | TestHub
- The unit digit in 1!+2!+3!+\ldots \ldots+4... | Mathematics | TestHub
- The number of numbers from 1 to 10^{6} (bo... | Mathematics | TestHub
- If \mathrm{n}>1 is the smallest integer wi... | Mathematics | TestHub
- Number of positive integral multiples does... | Mathematics | TestHub
- Consider n \times n graph paper where n is... | Mathematics | TestHub
- The number of divisors of the form 2 n+1(n... | Mathematics | TestHub
- Different words (anagrams) are formed usin... | Mathematics | TestHub
- Put numbers 1,2,3,4,5,6,7,8 at the vertice... | Mathematics | TestHub
- If number of numbers greater than 3000 , w... | Mathematics | TestHub
- Considering the rectangular hyperbola x y=... | Mathematics | TestHub
- If 7 identical red balls, 12 identical gre... | Mathematics | TestHub
- Nine hundred distinct n -digit numbers are... | Mathematics | TestHub
Group formation(9)
- The number of ways of distributing 8 ident... | Mathematics | TestHub
- This question has Statement and Statement... | Mathematics | TestHub
- The total number of ways in which 5 balls... | Mathematics | TestHub
- In how many ways can 5 prizes be distribut... | Mathematics | TestHub
- In a hotel, four rooms are available. Six... | Mathematics | TestHub
- Eight persons are to be transported from c... | Mathematics | TestHub
- Ifis the number of ways five different emp... | Mathematics | TestHub
- The number of different ordered triplets (... | Mathematics | TestHub
- The total number of ways of selecting 5 le... | Mathematics | TestHub
Miscellaneous/Mixed(7)
- Match the following List-I with List-IILis... | Mathematics | TestHub
- The number of distinct rational numbers of... | Mathematics | TestHub
- A cricket player played \mathrm{n}(\mathrm... | Mathematics | TestHub
- The number of divisors of 6912,52480,32000... | Mathematics | TestHub
- A cricket player played n(n>1) matches dur... | Mathematics | TestHub
- The number of 5 -digit numbers which are d... | Mathematics | TestHub
- Put numbers 1,2,3,4,5,6,7,8 at the vertice... | Mathematics | TestHub
nPr & nCr(172)
- Number greater than 1000 but less than 400... | Mathematics | TestHub
- Total number of four digit odd numbers tha... | Mathematics | TestHub
- Five digit number divisible by 3 is formed... | Mathematics | TestHub
- The number of ways in which 6 men and 5 wo... | Mathematics | TestHub
- A student is to answer 10 out of 13 questi... | Mathematics | TestHub
- If the letters of word SACHIN are arranged... | Mathematics | TestHub
- If are prime numbers and are the positive... | Mathematics | TestHub
- At an election, a voter may vote for any n... | Mathematics | TestHub
- The set is to be partitioned into three se... | Mathematics | TestHub
- The letters of the word are permuted and a... | Mathematics | TestHub
- In a shop there are five types of ice-crea... | Mathematics | TestHub
- From 6 different novels and 3 different di... | Mathematics | TestHub
- If , then lies in the interval | Mathematics | TestHub
- In a polygon no three diagonals are concur... | Mathematics | TestHub
- If , then equals to | Mathematics | TestHub
- There are two urns. Urn A has 3 distinct r... | Mathematics | TestHub
- If then is equal to | Mathematics | TestHub
- Let . The number of different ordered pair... | Mathematics | TestHub
- If the number of 5-element subsets of the... | Mathematics | TestHub
- Assuming the balls to be identical except... | Mathematics | TestHub
- The number of arrangements that can be for... | Mathematics | TestHub
- The number of positive integral solution of | Mathematics | TestHub
- 5 - digit numbers are to be formed using ,... | Mathematics | TestHub
- A box contains two white balls, three blac... | Mathematics | TestHub
- Letbe the number of all possible triangles... | Mathematics | TestHub
- Letbe an integer. Take n distinct points o... | Mathematics | TestHub
- Paragraph: Box contains three cards bearin... | Mathematics | TestHub
- The sum of the digits in the unit's place... | Mathematics | TestHub
- The number of all three elements subsets o... | Mathematics | TestHub
- An eight digit number divisible by 9 is to... | Mathematics | TestHub
- 8-digit numbers are formed using the digit... | Mathematics | TestHub
- In how many ways can a committee of 5 made... | Mathematics | TestHub
- Two women and some men participated in a c... | Mathematics | TestHub
- The total number of 4 -digit numbers in wh... | Mathematics | TestHub
- The number of points, having both co-ordin... | Mathematics | TestHub
- If in a regular polygon the number of diag... | Mathematics | TestHub
- The number of ways of selectingteams fromm... | Mathematics | TestHub
- Letandbe two sets containing four and two... | Mathematics | TestHub
- Letbe two sets containing seven and three... | Mathematics | TestHub
- The number of integers greater thanthat ca... | Mathematics | TestHub
- A debate club consists of 6 girls and 4 bo... | Mathematics | TestHub
- If all the words (with or without meaning)... | Mathematics | TestHub
- All the words that can be formed using alp... | Mathematics | TestHub
- If three vertices of a regular hexagon are... | Mathematics | TestHub
- If the four letter words (need not be mean... | Mathematics | TestHub
- A manhasfriends,of them are ladies andare... | Mathematics | TestHub
- The number of times the digitwill be writt... | Mathematics | TestHub
- If all the words, with or without meaning,... | Mathematics | TestHub
- The number of four letter words that can b... | Mathematics | TestHub
- -digit numbers are formed using only three... | Mathematics | TestHub
- If a parallelogram is cut by two sets ofli... | Mathematics | TestHub
- In a high school, a committee has to be fo... | Mathematics | TestHub
- The number of numbers betweenandthat can b... | Mathematics | TestHub
- - digit numbers are formed using only thre... | Mathematics | TestHub
- A group of students comprises ofboys and n... | Mathematics | TestHub
- A person writes letter to six friends and... | Mathematics | TestHub
- The number ofdigit number that can be form... | Mathematics | TestHub
- The Number of ways of choosingobjects out... | Mathematics | TestHub
- The number of natural numbers less thanwhi... | Mathematics | TestHub
- Let, then number of non-empty subsetsofsuc... | Mathematics | TestHub
- A committee ofmember is to be formed fromm... | Mathematics | TestHub
- If three of the six vertices of a regular... | Mathematics | TestHub
- All possible numbers are formed using the... | Mathematics | TestHub
- Suppose thatpillars of the same height hav... | Mathematics | TestHub
- There aremen and two women participating i... | Mathematics | TestHub
- Consider three boxes, each containingballs... | Mathematics | TestHub
- If the number of five digit numbers with d... | Mathematics | TestHub
- Total number of ways of selecting 2 white... | Mathematics | TestHub
- A test consists ofmultiple choice question... | Mathematics | TestHub
- Letbe an integer. Suppose that there areMe... | Mathematics | TestHub
- The number of words, with or without meani... | Mathematics | TestHub
- There aresections in a question paper and... | Mathematics | TestHub
- If the letters of the wordbe permuted and... | Mathematics | TestHub
- An urn containsred marbles,black marbles a... | Mathematics | TestHub
- The number of possible outcomes in a throw... | Mathematics | TestHub
- The number ofletter words (with or without... | Mathematics | TestHub
- The studentsare to be divided intogroupsan... | Mathematics | TestHub
- All the arrangements, with or without mean... | Mathematics | TestHub
- Let and If the total number of elements in... | Mathematics | TestHub
- The total number of-digit numbers whose gr... | Mathematics | TestHub
- How many numbers lying between 999 and 100... | Mathematics | TestHub
- If the sidesandof a trianglehaveandinterio... | Mathematics | TestHub
- The total number of two digit numbers, suc... | Mathematics | TestHub
- The number of-digit numbers which are neit... | Mathematics | TestHub
- The number of three-digit even numbers, fo... | Mathematics | TestHub
- The sum of all the elements in the setH.C.... | Mathematics | TestHub
- Consider a rectanglehavingpoints in the in... | Mathematics | TestHub
- Letbepoints on a circle. The number of dis... | Mathematics | TestHub
- The sum of all the-digit distinct numbers... | Mathematics | TestHub
- Teamconsists ofboys andgirls and Teamhasbo... | Mathematics | TestHub
- There areplayers in a cricket team, out of... | Mathematics | TestHub
- A scientific committee is to be formed fro... | Mathematics | TestHub
- The sum of all-digit numbers less than or... | Mathematics | TestHub
- Let. Then the number of elements in the se... | Mathematics | TestHub
- A number is called a palindrome if it read... | Mathematics | TestHub
- A natural number has prime factorization g... | Mathematics | TestHub
- Letbe a non-negative integer. Then the num... | Mathematics | TestHub
- Letand. Ifthen the sum of all the elements... | Mathematics | TestHub
- The total number of-digit numbers, whose g... | Mathematics | TestHub
- There are ten boysand five girlsin a class... | Mathematics | TestHub
- A class containsboys andgirls. If the numb... | Mathematics | TestHub
- The total number of three-digit numbers, w... | Mathematics | TestHub
- The number of natural numbers lying betwee... | Mathematics | TestHub
- The number of different seven-digit number... | Mathematics | TestHub
- The letters of the word 'MANKIND' are writ... | Mathematics | TestHub
- Considerboxes, where each box containsred... | Mathematics | TestHub
- Numbers are to be formed betweenand, which... | Mathematics | TestHub
- The number of-digit natural numbers, such... | Mathematics | TestHub
- The number of-digit numbers which are mult... | Mathematics | TestHub
- The total number of four digit numbers suc... | Mathematics | TestHub
- A person forgets his-digit ATM pin code. B... | Mathematics | TestHub
- Consider the square in the figure. Let be... | Mathematics | TestHub
- The letters of the word OUGHT are written... | Mathematics | TestHub
- The number of-letter words, with or withou... | Mathematics | TestHub
- All the letters of the word PUBLIC are wri... | Mathematics | TestHub
- Some couples participated in a mixed doubl... | Mathematics | TestHub
- Five digit numbers are formed using the di... | Mathematics | TestHub
- The sum of all the four-digit numbers that... | Mathematics | TestHub
- If the letters of the word MATHS are permu... | Mathematics | TestHub
- Let, and,. Then the sum of all the positiv... | Mathematics | TestHub
- The total number of three-digit numbers, d... | Mathematics | TestHub
- If all the six digit numberswithare arrang... | Mathematics | TestHub
- The total number of-digit numbers whose gr... | Mathematics | TestHub
- Let. The number of non-empty subsets oftha... | Mathematics | TestHub
- The total number of six digit numbers, for... | Mathematics | TestHub
- The number of integers, greater thanthat c... | Mathematics | TestHub
- How many different nine digit numbers can... | Mathematics | TestHub
- The number of numbers, strictly between an... | Mathematics | TestHub
- The number of ways of selecting two number... | Mathematics | TestHub
- Total numbers of-digit numbers that are di... | Mathematics | TestHub
- Letdigit numbers be constructed using the... | Mathematics | TestHub
- All words, with or without meaning, are ma... | Mathematics | TestHub
- Letandbe distinct integers whereand. Then,... | Mathematics | TestHub
- A boy needs to select five courses fromava... | Mathematics | TestHub
- The number of arrangements of all digits o... | Mathematics | TestHub
- If , then is equal to | Mathematics | TestHub
- In an examination of Mathematics paper, th... | Mathematics | TestHub
- If all the words with or without meaning m... | Mathematics | TestHub
- At an election a voter may vote for any nu... | Mathematics | TestHub
- The lines are distinct. For all the lines... | Mathematics | TestHub
- The total number of words (with or without... | Mathematics | TestHub
- The number of ways five alphabets can be c... | Mathematics | TestHub
- There are 5 points on the side , excluding... | Mathematics | TestHub
- The number of triangles whose vertices are... | Mathematics | TestHub
- The number of 3-digit numbers, formed usin... | Mathematics | TestHub
- There are 4 men and 5 women in Group A, an... | Mathematics | TestHub
- Let be the set of all seven-digit numbers... | Mathematics | TestHub
- There are 12 points in a plane, no three o... | Mathematics | TestHub
- The number of 6-letter words, with or with... | Mathematics | TestHub
- Let m and be two 2-digit numbers. Then the... | Mathematics | TestHub
- If the number of seven-digit numbers, such... | Mathematics | TestHub
- The number of different 5 digit numbers gr... | Mathematics | TestHub
- The number of sequences of ten terms, whos... | Mathematics | TestHub
- The number of natural numbers, between 212... | Mathematics | TestHub
- Line of slope 2 and line of slope intersec... | Mathematics | TestHub
- From a group of 7 batsmen and 6 bowlers, 1... | Mathematics | TestHub
- Group A consists of 7 boys and 3 girls, wh... | Mathematics | TestHub
- Let P be the set of seven digit numbers wi... | Mathematics | TestHub
- Let p be the number of all triangles that... | Mathematics | TestHub
- If all the words with or without meaning m... | Mathematics | TestHub
- The number of ways, in which the letters ,... | Mathematics | TestHub
- In a polygon, no three diagonals are concu... | Mathematics | TestHub
- The number of divisors of 2^{2} \cdot 3^{3... | Mathematics | TestHub
- The letters of the word COCHIN are permute... | Mathematics | TestHub
- The number of different permutations of al... | Mathematics | TestHub
- Number of arrangements of SYSTEMATIC in wh... | Mathematics | TestHub
- Let S=\{1,2,3, \ldots n\} , If X denote th... | Mathematics | TestHub
- The exponent of 7 in { }^{100} \mathrm{C}_... | Mathematics | TestHub
- The number of different words that can be... | Mathematics | TestHub
- Let \mathrm{A}=\{1,2,3,4,5,6,7\} . Then nu... | Mathematics | TestHub
- Let P be the product of distances of any v... | Mathematics | TestHub
- The number of 10 letter permutations compr... | Mathematics | TestHub
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