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Question

The number of even numbers greater than 100 that can be formed by the digits 0,1,2,3 ( no digit being repeated ) is

A
20
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B
30
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C
40
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D
None of these
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Solution

The correct option is C 20
The number can be of 3 or 4 digits.
To find the number of even numbers of three digits, the unit's place must be filled by 0 and 2.
Thus the number of even numbers of 3 digits (having or not having 0 in hundredth place) =2P1×3P2
But the number of even numbers of 3 digits having 0 at hundredth place =2P1 (as unit's place is naturally filled by 2 and ten's place by one of 1 and 3)
Thus the number of even numbers of 3 digits =2P1×3P22P1.....(1)
Similarly, the numbers of even numbers of 4 digits =2P1×3P32P2...(2)
Adding (1) and (2) we get, the number of even numbers greater than 100 =(2P1×3P22P2)+(2P1×3P32P2)=20

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