Question

From 5 faculty members, a committee of 2 is to be formed. In how many ways can this be done?

Answer 1

A committee of 2 from 5 faculty members can be formed in 10 different ways. This is computed using the combinations formula C(n, k) = n! / (k! * (n-k)!), where n is the total number of faculty members and k is the committee size.

Step-by-step explanation:

From 5 faculty members, a committee of 2 is to be formed. The number of ways this can be done is found by calculating combinations, since the order of selection does not matter. This is a combinatorial problem, often solved using the formula for combinations C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from, and k is the number of items to choose.

In this case, we have n = 5 faculty members and we want to choose k = 2 for the committee. The formula gives us:

1. Calculating the factorial of n: 5! = 5 * 4 * 3 * 2 * 1
2. Calculating the factorial of k: 2! = 2 * 1
3. Calculating the factorial of n-k: (5-2)! = 3! = 3 * 2 * 1
4. Applying the combination formula: C(5, 2) = 5! / (2! * (5-2)!) = (5 * 4) / (2 * 1) = 10

Therefore, there are 10 different ways to form a committee of 2 from 5 faculty members.