Question

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

• A. 90,000
• B. 100,000
• C. 30,240
• D. 69,760

Answer 1

Answer: (D)

69,760

Answer 2

Using the digits 0, 1, 2,.......,9 the number of five digit telephone numbers which can be formed is $10^{5}$.

(since repetition is allowed)

The number of five digit telephone numbers which have none of the digits repeated = $10P_{5} = 30240$

$\therefore$ The required number of telephone numbers

= $10^{5} - 30240 = 69760$.