How many 3 digit numbers can be formed from the digits 1,2,3,4 and 5 assuming that Repetition of the digits is allowed?

# How many 3 digit numbers can be formed from the digits 1,2,3,4 and 5 assuming that Repetition of the digits is allowed?

1. A
125 ways
2. B
100 ways
3. C
250 ways
4. D
50 Ways

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### Solution:

Here we have the digits 1,2,3,4,5 and we can repeat them to make a 3 digit number.
We can have any of the 5 digits for one place. So the number of ways to put a digit in the 1's place is 5.
We can have any of the 5 digits for the tens place because repetition is allowed. So the number of ways to replace the digit in the tens place is 5.
For the hundreds place we can have any of the 5 digits because repetition is allowed. So the number of ways to put a digit in the hundreds place is 5.
So the total number of paths is 555=125.
So option (1) is the correct answer.

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