To solve this problem, we will use the concept of combinations from combinatorics. A combination is a selection of items without regard to the order in which they are selected.

1. First, we need to select 2 freshmen out of 5. The number of ways to do this is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to select, and '!' denotes factorial. So, the number of ways to select 2 freshmen out of 5 is C(5, 2) = 5! / [2!(5-2)!] = 10.

2. Next, we need to select 3 sophomores out of 9. Using the same formula, the number of ways to do this is C(9, 3) = 9! / [3!(9-3)!] = 84.

3. Then, we need to select 4 juniors out of 8. The number of ways to do this is C(8, 4) = 8! / [4!(8-4)!] = 70.

4. Finally, we need to select 5 seniors out of 8. The number of ways to do this is C(8, 5) = 8! / [5!(8-5)!] = 56.

5. To find the total number of ways to form the committee, we multiply the number of ways to make each selection, because each selection is independent of the others. So, the total number of ways to form the committee is 10 * 84 * 70 * 56 = 32,448,000.

Question

To solve this problem, we will use the concept of combinations from combinatorics. A combination is a selection of items without regard to the order in which they are selected.

1. First, we need to select 2 freshmen out of 5. The number of ways to do this is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to select, and '!' denotes factorial. So, the number of ways to select 2 freshmen out of 5 is C(5, 2) = 5! / [2!(5-2)!] = 10.

2. Next, we need to select 3 sophomores out of 9. Using the same formula, the number of ways to do this is C(9, 3) = 9! / [3!(9-3)!] = 84.

3. Then, we need to select 4 juniors out of 8. The number of ways to do this is C(8, 4) = 8! / [4!(8-4)!] = 70.

4. Finally, we need to select 5 seniors out of 8. The number of ways to do this is C(8, 5) = 8! / [5!(8-5)!] = 56.

5. To find the total number of ways to form the committee, we multiply the number of ways to make each selection, because each selection is independent of the others. So, the total number of ways to form the committee is 10 * 84 * 70 * 56 = 32,448,000.

Knowee AI · Accepted Answer

To solve this problem, we will use the concept of combinations from combinatorics. A combination is a selection of items without regard to the order in which they are selected.

1. First, we need to select 2 freshmen out of 5. The number of ways to do this is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to select, and '!' denotes factorial. So, the number of ways to select 2 freshmen out of 5 is C(5, 2) = 5! / [2!(5-2)!] = 10.

2. Next, we need to select 3 sophomores out of 9. Using the same formula, the number of ways to do this is C(9, 3) = 9! / [3!(9-3)!] = 84.

3. Then, we need to select 4 juniors out of 8. The number of ways to do this is C(8, 4) = 8! / [4!(8-4)!] = 70.

4. Finally, we need to select 5 seniors out of 8. The number of ways to do this is C(8, 5) = 8! / [5!(8-5)!] = 56.

5. To find the total number of ways to form the committee, we multiply the number of ways to make each selection, because each selection is independent of the others. So, the total number of ways to form the committee is 10 * 84 * 70 * 56 = 32,448,000.

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 5 freshmen, 9 sophomores, 8 juniors, and 8 seniors are eligible to be on the committee, in how many ways can the committee be chosen?

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