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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 10810P8
At 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 =108
For 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 =10810P8
Hence, the answer is 10810P8.

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