Question

A civil air patrol unit of 13 members includes 5 officers.in how many ways can three members be selected for a search and rescue mission such that at least one officer is included

Answer 1

Answer: We can solve this problem by counting the total number of ways to select three members and then subtracting the number of ways to select three members without any officers.

The total number of ways to select three members from a group of 13 is given by the combination formula:

C(13,3) = 286

To count the number of ways to select three members without any officers, we need to choose three members from the 8 non-officers. This can be done in C(8,3) = 56 ways.

Therefore, the number of ways to select three members with at least one officer is:

C(13,3) - C(8,3) = 286 - 56 = 230

There are 230 ways to select three members for the search and rescue mission such that at least one officer is included.

Explanation: