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The number of 5 digit numbers such that the sum of their digits is even is?

2 Answers

1057
Ketan Chandak ·

There are 90,000 five digit numbers..in half of them sum of the digits will be even and likewise sum will be odd for the other half...so 45,000.

229
Dwijaraj Paul Chowdhury ·

sum of the digits to be even are in the.following cases
1). 4 odd and 1 even------5C4*5C1
2). 2 odd and 3 even---5C2*5C3
3) 5 even------5C5
therefore total no. of combinations---36(sum of the above cases)
the 5 digits will also permute in 36* 120 ways viz. 1080
but in 24 cases ,zero. will be the first digit
therefore no. of ways---1080-24=1056

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