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The number of four-digit numbers that ca...

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 a. `4^5-5!` b. `505` c. `600` d. none of these

A

`4^(5)-5!`

B

505

C

600

D

none of these

Text Solution

Verified by Experts

Required number of numbers = (Total number of 4 digit numbers with the digits 1, 2, 3, 4 and 5)-(Total number of 4-digit numbers with distinct digits formed with the digits 1, 2, 3, 4 and 5).
`:.` Required number of numbers
`=5^(4)-""^(5)C_(4)xx4!""=625-120=505`.
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