How many 4-digit numbers can be formed from the digits 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

Question: How many 4-digit numbers can be formed from the digits 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

Solution:
Number will be divisible by 5 if the last number is 5.
So, first number can be chosen in ⁴C₁ ways
= 4 ways
As the digit is not repeated
second number can be chosen in ³C₁
= 3 ways

As the digit is not repeated
third number can be chosen in ²C₁
= 2 ways

∴ Total ways = 4 × 3 × 2 ways
= 24 ways