A congressional committie has of 8 senators and 7 representatives. How many ways can a subcomittie of 6 be formed from the full committee if exactly 5 of the members must be senators?
To find the number of ways a subcommittee of 6 can be formed from the full committee with exactly 5 senators, we need to consider the different possibilities.
First, we choose 5 senators from the 8 available. This can be done in 8 choose 5 ways, which can be calculated as:
C(8, 5) = (8!)/(5!(8-5)!) = (8!)/(5!3!) = (8 * 7 * 6)/(3 * 2 * 1) = 56
Next, we need to choose 1 representative from the remaining 7 representatives. Since we only need to choose 1 person, the number of ways to do this is simply 7.
Finally, to determine the total number of ways a subcommittee of 6 can be formed with exactly 5 senators, we multiply the number of ways to choose the senators by the number of ways to choose a representative:
Total ways = C(8, 5) * 7 = 56 * 7 = 392
Therefore, there are 392 ways to form a subcommittee of 6 with exactly 5 senators from the full committee.