find the number of way of forming an executive committee of four, in a department consisting of 15 members, if a particular man must be in the committee
3C14
well, 14C3, but you get the idea.
To find the number of ways of forming an executive committee of four with a particular man in the committee, we can use the concept of combinations.
Step 1: Identify the number of choices for the particular man.
Since there is a specific man who must be in the committee, there is only one choice for this position.
Step 2: Identify the number of choices for the remaining three committee members.
Since the remaining committee members can be any of the 14 remaining members, we have 14 choices for the first member, 13 choices for the second member, and 12 choices for the third member.
Step 3: Calculate the total number of ways.
To get the total number of ways, we multiply the number of choices for each position together.
Total number of ways = 1 choice for the particular man * 14 choices for the first remaining member * 13 choices for the second remaining member * 12 choices for the third remaining member
Total number of ways = 1 * 14 * 13 * 12
Total number of ways = 2184
Therefore, there are 2184 ways of forming an executive committee of four in a department consisting of 15 members, with a particular man being in the committee.