A company's board of directors wants to form a committee of 2 of its members. There are 5 members to choose from. How many different committees of 2 members could possibly be formed?
To determine the number of different committees of 2 members that could be formed, we can use the formula for combinations:
C(n,r) = n! / (r!(n-r)!)
Where n is the total number of members in the group and r is the number of members to be selected for the committee.
In this case, there are 5 members to choose from and we want to form a committee of 2 members. Therefore, n=5 and r=2.
Plugging these values into the formula, we get:
C(5,2) = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4 * 3!) / (2! * 3 * 2)
= (5 * 4) / (2 * 1)
= 20 / 2
= 10
Therefore, there are 10 different committees of 2 members that could possibly be formed.
5C2 = 5! / [(5 - 2)! * 2!]
5 ways to pick the 1st member and 4 ways to pick the 2nd
... but ... Jane and Jim is the same as Jim and Jane
so ... (5* 4) / 2