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The number of five digit telephone numbe...

The number of five digit telephone numbers having at least one of their digits repeated is `90000` b. `100000` c. `30240` d. 69760

A

90000

B

10000

C

30240

D

69760

Text Solution

Verified by Experts

The correct Answer is:
D
If all the digits repeated, then number of 5-digit telephone numbers can be formed in `10^(5)` ways and if no digit repeated, then 5-digit telephone number can be formed in `""^(10)P_(5)` ways.
`therefore` Required number of ways `=10^(5) - ""^(10)P_(5) = 100000 - (10"!")/(5"!")`
`= 100000 - 10 xx 9 xx 8 xx 7 xx 6`
`= 100000 - 30240 = 69760`
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