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

Question:

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

(a) 90,000

(b) 10,000

(c) 30240

(d) 69760

Solution:

Total number of five digit telephone number possible without any restriction is 105 and number of 5 digit telephone number having all digits different is 10P5 

∴ Required number of ways i.e having at-least one digit repeated is =105 − 10P5

i.e 1000000 − 10 × 9 × 8 × 7 × 6

= 105 − 30240

= 69760

Hence, the correct answer is option D.

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