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How many three-digit numbers that are di...

How many three-digit numbers that are divisible by 5, can be formed, using the digit 0,2,3,5,7, if no digit occurs more than once in each number?

A

10

B

15

C

21

D

25

Text Solution

Verified by Experts

The correct Answer is:
C
If a number is divisible by 5, then the units digit must be either 0 or 5.
Case 1: If the units digit is 0, then the remaining two places can be done in `.^(4)P_(2)=12` ways.
Case 2: If the units digits is 5, then the remaining two places can be filled by the remaining 4 digits. It can be done in `3xx3=9` ways.
(`therefore` The hundreds place can not be filled with 0)
`therefore` The required number of 3-digit numbers=12+9=21.
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