A company's board of directors wants to form a committee of 3
of its members. There are 5
members to choose from. How many different committees of 3
members could possibly be formed?
5 choose 3 : )
Use your combination formula.
To find the number of different committees of 3 members that can be formed, we can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n - r)!)
where n is the total number of items to choose from, and r is the number of items to choose.
In this case, we have 5 members to choose from, and we want to form a committee of 3 members. So, we need to find C(5, 3).
Using the formula, substituting the values, we have:
C(5, 3) = 5! / (3!(5 - 3)!)
= 5! / (3! * 2!)
= (5 * 4 * 3!) / (3! * 2 * 1)
= 5 * 4 / (2 * 1)
= 10
Therefore, there are 10 different committees of 3 members that could possibly be formed.