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Q.

The number of numbers greater than 400000 that can be formed by using the digit 0, 2, 2, 4, 4, 5 is:

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a

90

b

32

c

20

d

None of the above

answer is A.

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Detailed Solution

There are 6 digits and the numbers greater than 400000 will have 6 digits. We have to use all 6 digits at a time, the numbers greater than 400000 will have either 4 or 5 at the extreme left position.
1. When 5 is at the extreme left position, the remaining 5 places can be filled with the digits 0,2,2,4,4. This can be done in

\frac{5!}{2! 2!} = 30 ways

2. When 4 occupies the extreme left position, then the remaining 5 places can be filled by 0,2,2,4,5 digits. This can be done in

\frac{5!}{2!} = 60

So total numbers greater than 400000 are 30+60 = 90

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