SOLUTION: In how many ways three integers be selected from integers 1,2,3,...30, so that there sum is even.

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Question 897333: In how many ways three integers be selected from integers 1,2,3,...30, so that there sum is even.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the possible combinations of evens and odds.
Even+Even=Even
Even+Odd=Odd
Odd+Odd=Even
So then
(Even+Even)+Even=Even
(Even+Odd)+Odd=Even
while
(Even+Even)+Odd=Odd
(Even+Odd)+Even=Odd
So then choose 3 even numbers or 1 even and 2 odds to get an even sum.