Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationnPr & nCrHard2 minPYQ_2021

MathematicsHardnumerical

The total number of $4$ -digit numbers whose greatest common divisor with $18$ is $3$ is _____.

Answer:

1000.00

Solution:

Let $N$ be the four digit number $g c d (N, 18) = 3$

Hence $N$ is an odd integer which is divisible by $3$ but not by $9$ .

$4$ digit odd multiples of $3$

$1005, 1011, \dots, 9999 \to 1500$

digit odd multiples of $9$

$1017, 1035, \dots, 9999 \to 500$

Hence number of such $N = 1500 - 500 = 1000$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: PYQ_2021

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