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NDA 2020 Maths · Mathematics · Permutations and Combinations · hard

How many three-digit numbers divisible by 5 can be formed from the digits 0, 2, 5, 7, 9 if no digit is repeated?

Single correct option

How many three-digit numbers divisible by 5 can be formed from the digits 0, 2, 5, 7, 9 if no digit is repeated?
  1. A. 24
  2. B. 30
  3. C. 21
  4. D. 12
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Answer: (C) 21

A number divisible by 5 ends in 0 or 5. Ending in 0: 4×3=124\times3=12. Ending in 5: the hundreds digit is non-zero from {2,7,9}\{2,7,9\} (3 ways) and the tens digit comes from the 3 remaining digits (3 ways), giving 9. Total 12+9=2112+9=21.
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Original question written in the NDA 2020 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