Question

How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are not allowed?

Answer 1

The repetition of digits are not allowed.

The given digits are 0, 1, 2, 3, 4, 5.

A number will be divisible by 5

if the digit in the unit place is 0 or 5

So the unit place can be filled by 0 or 5

(a) When the unit place is 0 it is filled in 1 way

And so 10’s place can be filled in 5 ways (by using 1, 2, 3, 4, 5)

And 100’s place can be filled in (5 – 1)4 ways

So the number of 3 digit numbers with unit place 0 = 1 × 5 × 4 = 20

(b) When the unit place is 5 it is filled in 1 way

Since 0 is given as a digit to fill 100’s place 0 should be excluded

So 100’s place can be filled in (excluding 0 and 5)4 ways

And 10’s place can be filled in (excluding 5 and one digit and including 0)4 ways

So the number of 3 digit numbers with unit place 5 = 1 × 4 × 4 = 16

∴ Number of 3 digit numbers ÷ by 5 = 20 + 16 = 36