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Question

The number of numbers lying between 99 and 1000 which can be formed using the digits 2, 3, 7, 0, 6, 8 when no digit is being repeated is


A
102
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B
120
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C
100
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D
None of these
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Solution

The correct option is C 100

Digits are 2, 3, 7, 0, 6, 8 i.e. six in all.
We have to form a number between 99 and 1000. Clearly, they will be of three digits and their number will be
6P3=6×5×4=120
Out of these, we have to exclude those numbers of 3 digits which have zero in the first place.
When the first place is filled by 0, remaining numbers can be arranged in 5P2 ways.
Their number is 5P2=5×4=20
The required number is 120-20=100


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