SOLUTION: Out of thirty consecutive integers, how many ways can three numbers be selected whose sum is odd?

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Question 1149515: Out of thirty consecutive integers, how many ways can three numbers be selected whose sum is odd?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


To get an odd sum with three integers, you need either 3 odd integers or 2 even and 1 odd.

In any 30 consecutive integers, there are 15 odd and 15 even integers. So

C(15,3)+C(15,2)*C(15,1) = 455+105*15 = 2030