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# How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4, 5, 6, 7, 8 if repetition of digits is allowed?

Given: We have 5 digits, i.e. 4,5,6,7,8

To Find: Number of numbers divisible by 5

Condition: (i) Number should be between 4000 and 5000

(ii) Repetition of digits is allowed

Here as the number is lying between 4000 and 5000, we can conclude that the number is of 4-digits and the number must be starting with 4.

Now, for a number to be divisible by 5 must ends with 5

Let us represent the 4-digit number

Therefore,

The first place is occupied by 4 = 1 way

The fourth (last) place is occupied by 5 = 1 way

The second place can be filled by 5 numbers = 5 ways

The third place can be filled by 5 numbers = 5 ways

Total numbers formed = 1 × 5 × 5 × 1 = 25

There are 25 numbers which are divisible by 5 and lying between 4000 and 5000 and can be formed from the digits 4, 5, 6, 7, 8 with repetition of digits.

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