The number of five-digit telephone numbers having at least one of… - Vidyadip

MCQ

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

A
90000.
B
100000.
C
30240.
✓
69760

✓

Answer

Correct option: D.

69760

Total number of five digit numbers (since there is no restriction of the number 0XXXX) = 10 × 10 × 10 × 10 × 10 = 100000.
These numbers also include the numbers where the digits are not being repeated. So, we need to subtract all such numbers.
Number of 5 digit numbers that can be formed without any repetition of digits = 10 × 9 × 8 × 7 × 6 = 30240
$\therefore$ Number of five-digit telephone numbers having at least one of their digits repeated = {Total number of 5 digit numbers} - {Number of numbers that do not have any digit repeated} = 100000 - 30240 = 69760

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