Mark the correct alternative in the following:
The number of five-digit telephone numbers having at least one of their digits repeated is
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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