The total number of 5-digit telephone numbers | vedclass

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(C) The first digit cannot be $0$.The total number of $5$-digit numbers is $9 	imes 10 	imes 10 	imes 10 	imes 10 = 90,000$.The number of $5$-digi

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$62784$

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(C) The first digit cannot be $0$.The total number of $5$-digit numbers is $9 	imes 10 	imes 10 	imes 10 	imes 10 = 90,000$.The number of $5$-digit numbers where no digit is repeated is calculated as follows:For the first position,there are $9$ choices $(1-9)$.For the second position,there are $9$ choices ($0-9$ excluding the first digit).For the third position,there are $8$ choices.For the fourth position,there are $7$ choices.For the fifth position,there are $6$ choices.Total numbers with no repetition $= 9 	imes 9 	imes 8 	imes 7 	imes 6 = 27,216$.The number of $5$-digit numbers with at least one digit repeated is the total number of $5$-digit numbers minus the number of $5$-digit numbers with no repetition.$= 90,000 - 27,216 = 62,784$.

The total number of $5$-digit telephone numbers that can be formed such that at least one digit is repeated is .... (The first digit cannot be $0$).

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