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Question

# How many 8 digit mobile numbers can be formed if at least one digit is repeated?

A
108
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B
107
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C
10810P7
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D
10810P8
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Solution

## The correct option is D 108−10P8At least one digit is repeated = Total − No. digit is repeated For total permutations,Any of the digit can be filled by any of the 10 numbers.⇒ Total =10×10.......8 times =108For no digit to be repeated: Let first digit be any of the 10 numbers,Next digit can be any of the 9 remaining and so on.....=10×9×8×7×6×5×4×3=10P8⇒ Required =108−10P8Hence, the answer is 108−10P8.

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