How many 4-digit numbers can be formed from the digits 2, 4, 5, 7, and 8, which are divisible by 4, and none of the digits is repeated?

Question: How many 4-digit numbers can be formed from the digits 2, 4, 5, 7, and 8, which are divisible by 4, and none of the digits is repeated?

Solution:
A number is divisible by 4 if the last two digits of the number form a number divisible by 4.
The valid two-digit numbers divisible by 4, using the digits 2, 4, 5, 7, and 8 are: 24, 28, 48, 52, 72, 84 = 6 ways

So, first number can be chosen in = ³C₁ ways
= 3 ways

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

∴ Total ways = (6 × 3 × 2) ways
= 36 ways