QUESTION

# How many 3 digit numbers can be formed from the digits 0, 1, 2, 3 and 4 with repetitions?

Hint: In this question the rightmost digit of the 3 digits number can be chosen from 5 digits that is 0, 1, 2, 3 and 4, now the left to this digit or the tenth place can be again chosen from the same 5 digits, now the hundredth place digit can only be chosen from 4 digits as 0 can’t be the first digit of a number.

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Total number of ways = $4 \times 5 \times 5$ = $100$
Note: In this question it’s provided with repetition, this means that the digits once used are available to be used again however if this would not have been the case then the unit’s place could have been chosen from 5 digits that is 0, 1, 2, 3 and 4, then the tenth digits should have been chosen from 4 digits as 1 digits is already being used for the unit’s place and then the hundredth place could have been chosen from 2 digits as 2 digits are already been chosen previously and we can’t chose 0 as the first digits of a number thus the answer in that case would have been $2 \times 4 \times 5$.