Mathematics - Permutation & Combination Question with Solution | TestHub
Among the integers from 1 to 1000, inclusive, match each count. Column I: (A) Divisible by at least one of 10, 15, 25 (B) Divisible by none of 10, 15, 25 (C) Divisible by at least two of 10, 15, 25 (D) Divisible by exactly two of 10, 15, 25 Column II: (p) 54 (q) 48 (r) 146 (s) 352 (t) 854
Column I | Column II |
|---|---|
(A) Divisible by at least one of 10, 15, 25 | (p) 54 |
(B) Divisible by none of 10, 15, 25 | (q) 48 |
(C) Divisible by at least two of 10, 15, 25 | (r) 146 |
(D) Divisible by exactly two of 10, 15, 25 | (s) 352 |
| (t) 854 |
Options:
Answer:
Solution:
This repeats Q6. Multiples of 10,15,25 number 100,66,40; pairwise intersections number 33,20,13, and the triple intersection numbers 6. Inclusion-exclusion gives the union 146, its complement 854, at least two 33+20+13-2(6) = 54, and exactly two .
