Question

[amc8.1996.21] how many subsets containing three different numbers can be selected from the set\[\{ 89,95,99,132, 166,173 \}\] so that the sum of the three numbers is even?

Answer 1

12

Explanation:

we have four odd numbers 89, 95, 99, 173, and two even numbers 132 and 166.

the cases where the sum of three numbers is even is: e/e/e and o/o/e.

e/e/e isn't possible since there are only two even numbers.

the other alternative is o/o/e, so we take 2 odd numbers and 1 even number.

this is equivalent to 4C2 × 2C1 = 6 × 2 = 12

so, there are 12 subsets.