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Question
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
Options
90,000
10,000
30,240
69,760
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Solution
The number of 5-digit telephone numbers having atleast one of their digits repeated is 69,760.
Explanation:
Total number of 5-digit telephone number if all the digits are repeated = (10)5 ......[∵ Digits are from 0 to 9]
If digits are not repeated, then 5-digit telephones, can be formed in 10P5 ways
∴ Required number of ways = (10)5 – 10P5
= `100000 - (10!)/((10 - 5)!)`
= `100000 - (10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5!)`
= 100000 – 30240
= 69760
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