NDA 2016 Maths · Mathematics · Permutations and Combinations · hard

The number of three-digit numbers with all digits distinct that are divisible by 5 is

Single correct option

The number of three-digit numbers with all digits distinct that are divisible by

5

A. $136$
B. $144$
C. $128$
D. $180$

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Answer: (A) $136$

The last digit is 0 or 5. If it is 0, the first two places can be filled in

9\times8=72

ways. If it is 5, the first digit cannot be 0 or 5, giving 8 choices, and the middle digit has 8 choices (any digit except the two used, including 0), so

8\times8=64

. Total

72+64=136

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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake