Q. 25.0( 4 Votes )

Mark the correct alternative in the following:

The number of five-digit telephone numbers having at least one of their digits repeated is

A. 90000

B. 100000

C. 30240

D. 69760

Answer :

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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