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

Answer 1

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.