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How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?

  1. 0
  2. 1
  3. 3
  4. 4

Answer

A five-digit number is divisible by 125, if the last three digits are divisible by 125. So the possible last three digits are 375 and 875.

5 should come in unit’s place, and 7 should come in ten’s place.

Thousand’s place should contain 3 or 8. You can do it in 2! ways.

Remaining first two digits, you can arrange in 2! ways.

So you can have 2! × 2! = 4 such numbers.

These are: 23875, 32875, 28375, 82375.

The correct option is D.