Problema Solution
A company’s board of directors wants to form a committee of 3 of its members. There are 4 members to choose from. How many different committees of 3 members could possibly be formed?
Answer provided by our tutors
Since the order of the selected players is not of importance we will use combinations to solve.
The number of p-combinations from a set of n elements is:
In our case p = 3 and n = 4
We need to find the number of 3-combinations from a set of 4 elements:
C(4,3) = 4!/(3!(4-3)!)
C(4, 3) = 4!/(3!1!)
C(4, 3) = 4
There are 4 different committees of 3 members that could be possibly formed.
You can also denote the members as A, B, C and D and write down all the possible committees and that would be all the possible subsets of 3 elements of the set {A, B, C, D}:
{A, B, C}
{A, B, D}
{A, C, D}
{B, C, D}