The different six digit numbers whose 3 digits are even and 3 digits are odd is
A
281250
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B
281200
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C
156250
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D
none of these
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Solution
The correct option is D 281250 If first digit is even then select other places from remaining five places for two more even digits. This can be 4×5C2×5×5.
Now the remaining three places are to be fit up by odd digit which can be done in 53 ways. In this way number of six digit number in which three digit are even and 3 are odd in which three digit are even and 3 are odd in which the first digit is even =4×5C2×5×5×53=8×56 (0 can't occurs at first place) Similarly number of six digit numbers which begin with an odd number/digit and which have 3 even, 3 odd digits
=5×5C2×5×5×53=5×10×55=10.56 ∴ Total six digit number in which 3 odd 3 even are