Find the number of ways of forming an executive committee of 4 in a social club consisting of 15 members, if a particular man must be in the team
So, one is chose, leaving 14 others to those from.
Number of ways = C(14,3) = 364
Find the number of ways of forming an executive committee of four, in a department consisting of 15 member, if a particular man must be in the committee
the ANSWER is 14C3 =364
To find the number of ways of forming an executive committee of 4 in a social club consisting of 15 members, with a particular man being included, you can follow these steps:
1. Identify the number of choices for the particular man. In this case, since he must be included in the committee, there is only one choice for the particular man.
2. Determine the number of choices for the remaining 3 committee members. Since there are 14 members left (excluding the particular man), you need to select 3 committee members from a group of 14. You can use the concept of combination to find this number. The formula for combination is given by nCr = n! / (r!(n-r)!), where n is the total number of elements, r is the number of elements to be selected, and ! denotes factorial.
Using the combination formula, the number of choices for the remaining 3 committee members would be 14C3 = 14! / (3!(14-3)!) = (14 * 13 * 12) / (3 * 2 * 1) = 364.
3. Multiply the number of choices for the particular man with the number of choices for the remaining committee members to get the total number of ways. In this case, the number of ways would be 1 * 364 = 364.
Therefore, there are 364 ways of forming an executive committee of 4 in the social club, considering a particular man must be included.