A musician plans to perform 6 selections for a concert. If he can choose from 8 different pieces, how many ways can he arrange his program?
He chooses
the first piece from 8 pieces,
the second from 7,
the third from 6,
...
the 6th from 3.
So the number of choices would be
7*6*5...*3, but don't forget the encore.
Thanks for the help!
You're welcome!
To find the number of ways the musician can arrange his program, we can use the concept of permutations. The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where n is the total number of items and r is the number of items being chosen.
In this case, the musician has 8 different pieces to choose from and wants to perform 6 selections. Therefore, we can substitute n = 8 and r = 6 into the formula:
P(8, 6) = 8! / (8 - 6)!
First, we calculate the factorial of each number. The factorial of a number is the product of all positive integers less than or equal to that number.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 40,320
(8 - 6)! = 2!
2! = 2 x 1
= 2
Substituting these values into the formula:
P(8, 6) = 40,320 / 2
P(8, 6) = 20,160
Therefore, there are 20,160 different ways the musician can arrange his program.