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(#M40018504) SELF question urgent Keep an EYE

how many 8 digit nos are there the sum of whose digit is even?

naina (11 years ago)

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Vinay Sipani   (11 years ago)

43906250

All are even => (5^8 - 5^7) numbers ------------(1)
Here negative part 5^7 represents numbers with 0 as first digit

Two are odd => 8C2*(5^4)*5^6 - 7C2*(5^2)*5^5 -------------(2)

Four are odd => 8C4*(5^4)*5^4 - 7C4*(5^4)*5^3 -------------(3)

Six are odd => 8C6*(5^6)*5^2 - 7C6*(5^6)*5 ----------------(4)

All are odd => 5^8 -----------(5)

=> Total possibilities = (1) + (2) + (3) + (4) + (5)
= 43906250 ways

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devendra  (11 years ago)

9*10*10*10*10*10*10*5*5

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naina  (11 years ago)

but ans is 45.10^6

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