Question

how many subsets containing three different numbers can be selected from the set 89, 95, 99, 132, 166, 173 so that the usm of the three numbers is even?

Answer 1

There are 12 subsets containing three different numbers from the given set such that the sum of the three numbers is even.

To solve this problem

The characteristics of odd and even numbers can be examined.

• Numerical oddities: {89, 95, 99, 173}
• Positive integers: {132, 166}

Two even and four odd numbers are present.

Let's now examine the cases:

• Three non-even numbers: There are four odd numbers, hence there are four ways to select three odd numbers.
• Two even numbers and one odd number: There are 2 even numbers and 4 odd numbers, so the number of ways to choose 2 even numbers and 1 odd number is 2 × 4= 8.

The total number of subsets containing three different numbers with an even sum is the sum of the above two cases: 4 + 8 = 12.

So, there are 12 subsets containing three different numbers from the given set such that the sum of the three numbers is even.