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Byju's Answer
Standard XII
Mathematics
Factorial
How many 8 ...
Question
How many
8
digit mobile numbers can be formed if at least one digit is repeated?
A
10
8
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B
10
7
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C
10
8
−
10
P
7
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D
10
8
−
10
P
8
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Solution
The correct option is
D
10
8
−
10
P
8
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
=
10
8
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
=
10
P
8
⇒
Required
=
10
8
−
10
P
8
Hence, the answer is
10
8
−
10
P
8
.
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