The number of four-digit numbers that can be | vedclass

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(B) The total number of four-digit numbers that can be formed using the digits $1, 2, 3, 4,$ and $5$ with repetition allowed is $5^4 = 625$.The number

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$505$

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(B) The total number of four-digit numbers that can be formed using the digits $1, 2, 3, 4,$ and $5$ with repetition allowed is $5^4 = 625$.The number of four-digit numbers with all distinct digits is given by the permutation formula $P(5, 4) = 5 	imes 4 	imes 3 	imes 2 = 120$.The number of four-digit numbers in which at least two digits are identical is the total number of four-digit numbers minus the number of four-digit numbers with all distinct digits.Required number $= 625 - 120 = 505$.

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4,$ and $5$ such that at least two digits are identical is

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