# Mark the correct alternative in the following:The number of five-digit telephone numbers having at least one of their digits repeated isA. 90000B. 100000C. 30240D. 69760

Total number of five-digit telephone numbers = 105 = 100000.

When no digit is repeated, then the number of five-digit telephone numbers = 10P5

[as, 5 digits among 10 digits can be arranged in 10P5 ways]

=10×9×8×7×6

= 30240

So, the number of five-digit telephone numbers having at least one of their digits repeated is = 100000 – 30240

= 69760.

The discussion can be shown pictorially as:

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