The number of 4-digit numbers that can be made with the digits 1,2,3,4 and 5 in which at least two digits are identical, is

4^{5} - 5!

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505

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600

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none of these

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Solution

The correct option is A 505
First we'll calculate the number of ALL 4-digit numbers that can
be made with them. Then we'll calculate and subtract the number
of 4-digit numbers that don't have any of the digits identical.
To find all possible 4-digit numbers that can be made.
1. There are $5^{4}$ ways $= 625$ ways to choose the 1st 4 digits,
which is all of them.
Now we must subtract the number of ways in which there are no two digits alike
$= 5!$ ways $= 120$ ways to choose the 1st 4 digits, which is all of them.
So $=> 625 - 120 = 505$

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