The number of 5 digit telephone numbers havin | vedclass

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(D) The total number of $5$ digit telephone numbers that can be formed using the digits $0, 1, 2, ..., 9$ is $10^5 = 100000$ (since each of the $5$ po

Vedclass · Accepted Answer

$69760$

Vedclass · Answer

(D) The total number of $5$ digit telephone numbers that can be formed using the digits $0, 1, 2, ..., 9$ is $10^5 = 100000$ (since each of the $5$ positions can be filled by any of the $10$ digits).The number of $5$ digit telephone numbers where no digit is repeated is given by the permutation formula $^{10}P_5 = 10 	imes 9 	imes 8 	imes 7 	imes 6 = 30240$.The number of telephone numbers having at least one digit repeated is the total number of telephone numbers minus the number of telephone numbers with no repeated digits.Required number $= 100000 - 30240 = 69760$.

The number of $5$ digit telephone numbers having at least one of their digits repeated is

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