# Thread: 5-digit numbers which have exactly two identical digits.

1. ## 5-digit numbers which have exactly two identical digits.

How many 5-digit numbers are possible which have exactly two identical digits (For example 1224 has exactly two identical digits)?
OPTIONS

1) 3024
2) 12096
3) 30240
4) 45360
5) 42336

2. ## Re: probability

Originally Posted by gokulavasan
How many 5-digit numbers are possible which have exactly two identical digits (For example 1224 has exactly two identical digits)?
OPTIONS

1) 3024
2) 12096
3) 30240
4) 45360
5) 42336
If you allow the numbers to start with zero, you need to count the number of ways the repeated digit can be placed within the 5 available digits, then multiply that by 10 for the number of possible digits that the repeated digit can be. Now multiply by the number of ways of filling in the remaining 3 digits.

This is for numbbers that can start with a zero, but of the numbers found 0.1 of them start with a zero, so multiply what you found above by 0.9 to get the answer.

CB

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### find the number of 4 digit numbers starting with 1 and having exactly two identical digits

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