A musician plans to perform 5 selections for a concert. If he can choose from 8 different pieces, how
many ways can he arrange his program?
To find the number of ways the musician can arrange his program, we need to use the concept of permutations.
The number of ways to arrange the program is given by the formula for permutations: nPr = n! / (n - r)!
In this case, the musician has 8 different pieces to choose from for each selection, and he plans to perform 5 selections.
Using the formula, we have:
n = 8 (number of choices for each selection)
r = 5 (number of selections)
So, the number of ways to arrange the program is:
8P5 = 8! / (8 - 5)!
= 8! / 3!
= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1)
= 8 x 7 x 6 x 5 x 4
= 6720
Therefore, there are 6720 different ways the musician can arrange his program.
To find the number of ways the musician can arrange his program, we can use the concept of permutations.
The number of permutations of selecting k items from n items is given by the formula:
P(n, k) = n! / (n-k)!
In this case, the musician plans to perform 5 selections out of 8 different pieces. So we need to calculate P(8, 5).
To calculate n!, which means the factorial of n, we multiply all positive integers from 1 to n. In our case, we need to find 8!.
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
Similarly, to calculate (n-k)!, we need to find (8-5)!, which is 3!.
3! = 3 * 2 * 1 = 6
Now, we can substitute these values into the permutation formula:
P(8, 5) = 8! / (8-5)!
= 40,320 / 6
= 6,720
Therefore, there are 6,720 ways the musician can arrange his program.
Assuming he doesn't play the same thing twice: 8 x 7 x 6 x 5 x 4 = __
That can also be written 8!/3!