Question

A certain congressional committee consists of 14 senators and 14

representatives. How many ways can a subcommittee of 6 be formed if
at least 4 of the members must be senators?

Answer 1

To form a subcommittee of 6 with at least 4 senators, we consider two cases: 4 senators and 2 representatives, and 5 senators and 1 representative. We then calculate the number of ways for each case and add them together to get the total number of ways.

Step-by-step explanation:

To calculate the number of ways a subcommittee of 6 can be formed with at least 4 senators, we need to consider two cases: 4 senators and 2 representatives, and 5 senators and 1 representative.

For the first case, the number of ways to choose 4 senators from 14 is C(14, 4) and the number of ways to choose 2 representatives from 14 is C(14, 2). Multiplying these two quantities gives us the number of ways for the first case.

For the second case, the number of ways to choose 5 senators from 14 is C(14, 5) and the number of ways to choose 1 representative from 14 is C(14, 1). Multiplying these two quantities gives us the number of ways for the second case.

Finally, we add the number of ways from the two cases to get the total number of ways a subcommittee of 6 can be formed with at least 4 senators.