The number of four-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 B $505$
The number of numbers when repetition is allowed is $5^{4}$ .
The number of numbers when digits cannot be repeated is $^{5} P_{5}$ .
Therefore, the required number of numbers is $= 5^{4} - 5! = 505$ .

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

The correct option is B 505The number of numbers when repetition is allowed is 54.The number of numbers when digits cannot be repeated is 5P5.Therefore, the required number of numbers is =54−5!=505.

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

The correct option is B $505$
The number of numbers when repetition is allowed is $5^{4}$ .
The number of numbers when digits cannot be repeated is $^{5} P_{5}$ .
Therefore, the required number of numbers is $= 5^{4} - 5! = 505$ .