Using Combination,
Total 12 possible 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.
We have given a set say S which contains 6 elements, S = {89, 95, 99, 132, 166, 173}
we want to select three numbers from S such that sum of these is even .
To have an even sum with three numbers, we must add either E+O+O, or E + E + E
where O ---> an odd number
E ---> an even number.
Since there are not three even numbers in the given set, case E+E+E is not possible. Thus, we must choose two odd numbers, and one even number.
There are 2 choices for the even number.
There are 4 choices for the first odd number. There are 3 choices for the last odd number. But the order in which we pick these 2 numbers doesn't matter, so this overcounts the pairs of odd numbers by a factor of 2. Thus, we have ⁴C₂ = 4×3/2 = 6 choices for a pair of odd numbers.
In total, there are 2 choices for an even number, and 6 choices for the odd numbers,
Hence, the total of 2×6 = 12 possible choices for a 3-element set that has an even sum.
To learn more about Combination formula refer:
https://brainly.com/question/11732255
#SPJ4
