Question

A group of Mathematics faculty at the local college consists of 6 women and 9 men. Five people are to be selected to go to a conference. How many different ways can a group of five people be selected from this group of 15?

Answer 1

There are 3003 different ways to select a group of five people from a group of 15 faculty members using the combination formula C(15, 5).

Step-by-step explanation:

To determine how many different ways a group of five people can be selected from a group of 15 faculty members consisting of 6 women and 9 men at a local college, we use combinatorics. This problem is an example of a combination where order does not matter and each person can only be chosen once. The formula for combinations is given by C(n, k) = n! / (k! * (n - k)!), where 'n' is the total number of items, 'k' is the number of items to choose, and the '!' signifies a factorial which is the product of all positive integers up to that number.

In this case, n = 15 faculty members and k = 5 people to be selected. Therefore, the number of different combinations is:

C(15, 5) = 15! / (5! * (15 - 5)!)
= 15! / (5! * 10!)
= (15 × 14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)
= 3003

So, there are 3003 different ways a group of five people can be selected from this group of 15 faculty members.