Question

How many five digit numbers can be formed using 0 1 2 3 4 5 and divisible by 4

Answer 1

Answer:

144 numbers if repetition is not allowed.

875 numbers if repetition is allowed.

Step-by-step explanation:

1) Repetition is not allowed.

If the number is divisible by 4, the following should be come at the end of the number.

04, 12, 20, 24, 32, 40, 52 (7 chances to be at the last. )

With 04 or 20 or 40 at the end, we can make 4 × 3 × 2 × 3 = 72 numbers.

With 12 or 24 or 32 or 52, we can make 3 × 3 × 2 × 4 = 72 numbers.

Totally, we can make 72 + 72 = 144 numbers.

2) Repetition is allowed.

If the number is divisible by 4, the following should be come at the end of the number.

04, 12, 20, 24, 32, 40, 52 (7 chances to be at the last. )

∴ Totally, we can make 5 × 5 × 5 × 7 = 875 numbers.