A club consists of 8 seniors, 7 juniors, and 4 sophomores. A subcommittee consisting of 3 seniors, 2 juniors, and 1 sophomore will be chosen. How many different such subcommittees are there?
C(8,3)*C(7,2)*C(4,1) = 56*21*4=4704
Well, let's do the math. To form the subcommittee, you need to choose 3 seniors out of 8 (8 choose 3), 2 juniors out of 7 (7 choose 2), and 1 sophomore out of 4 (4 choose 1).
So, the total number of different subcommittees is (8 choose 3) * (7 choose 2) * (4 choose 1), which is equal to the product of those three combinations.
Now, if you want me to calculate the actual number, I'll have to put on my math hat and do some calculations. Gimme a moment, I need to find my math hat... where did I put it... ah, here it is!
After putting on my math hat, the total number of different subcommittees is 56 * 21 * 4, which equals 4704. So, there are 4704 different subcommittees that can be formed.
To find the number of different subcommittees that can be chosen, we need to calculate the combinations of each class level.
First, let's calculate the number of ways to choose 3 seniors out of 8. We can use the formula for combinations, denoted as C(n, r):
C(8, 3) = 8! / (3! * (8-3)!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
Next, let's calculate the number of ways to choose 2 juniors out of 7:
C(7, 2) = 7! / (2! * (7-2)!) = (7 * 6) / (2 * 1) = 21
Lastly, the number of ways to choose 1 sophomore out of 4:
C(4, 1) = 4! / (1! * (4-1)!) = 4 / (1 * 1) = 4
Now, we need to find the total number of subcommittees by multiplying the three combinations calculated:
Total number of subcommittees = C(8, 3) * C(7, 2) * C(4, 1)
= 56 * 21 * 4
= 4704
Therefore, there are 4,704 different subcommittees that can be chosen.
To find the number of different subcommittees that can be chosen, we need to calculate the combinations of seniors, juniors, and sophomores separately, and then multiply them together to get the total number of possibilities.
The number of ways to choose 3 seniors from a group of 8 can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of seniors (8) and r is the number of seniors needed for the subcommittee (3).
Using this formula, we can calculate:
C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = (8 * 7 * 6) / (3 * 2 * 1) = 8 * 7 = 56
So there are 56 different ways to choose 3 seniors.
Similarly, we can calculate the number of ways to choose 2 juniors from a group of 7:
C(7, 2) = 7! / (2!(7-2)!) = 7! / (2!5!) = (7 * 6) / (2 * 1) = 7 * 3 = 21
And the number of ways to choose 1 sophomore from a group of 4:
C(4, 1) = 4! / (1!(4-1)!) = 4! / (1!3!) = 4 / 1 = 4
To find the total number of different subcommittees, we multiply these three values together:
Total subcommittees = (Number of ways to choose seniors) * (Number of ways to choose juniors) * (Number of ways to choose sophomores)
= 56 * 21 * 4
= 4704
So there are 4704 different subcommittees that can be chosen.