Question

in a photography class, there are 8 students, and the instructor wants to create a committee of 3 students to organize a photography class. how many different committees can be formed if the order of selection matters?

Answer 1

To determine the number of different committees that can be formed from 8 students, taking 3 at a time, where order matters, you use the permutation formula resulting in 336 different committees.

Step-by-step explanation:

The student's question involves calculating the number of different committees that can be formed from 8 students, choosing 3, where the order of selection matters.

This is a permutation problem because the order of selection is important.

1. First, we recognize that the problem is a permutation because the order of the committee members is important.
2. To calculate the number of permutations of 8 students taken 3 at a time, we use the permutation formula P(n, k) = n! / (n-k)! where n is the total number of objects to choose from, and k is the number of objects chosen.
3. Plugging in the numbers, we calculate P(8, 3) = 8! / (8-3)! which simplifies to 8! / 5!.
4. Finding the factorial of these numbers, 8! = 8 x 7 x 6 x 5! and since 5! cancels out, we're left with 8 x 7 x 6, which equals 336.

Therefore, there are 336 different committees that can be formed if the order of selection matters.