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Three different numbers are chosen from 1, 2, 3, …, 20. In how many ways can they be chosen so that their sum is even?

Competition practicePermutations & Combinations

A570
B1140
C450
D600

Step-by-Step Solution

There are 10 even and 10 odd numbers. Even sum: all three even,

^{10} C_{3} = 120

; or two odd and one even,

^{10} C_{2} \times 10 = 450

. Total

570

.

Answer: A) 570

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