The student council is putting on a school talent show. Sam, Ellie, Tim, and Jake have each signed up to perform. In how many different orders can the program be arranged?
Question
The student council is putting on a school talent show. Sam, Ellie, Tim, and Jake have each signed up to perform. In how many different orders can the program be arranged?
Solution
This is a permutation problem. Permutations are the number of ways a subset of a specified size can be arranged from a given set, generally without replacement, where the order of selection does matter.
In this case, we have 4 students (Sam, Ellie, Tim, and Jake) and we want to know how many different orders they can perform in.
The formula for permutations is:
P(n, r) = n! / (n-r)!
where:
- n is the total number of options,
- r is the number of selections to be made, and
- "!" denotes a factorial, meaning the product of all positive integers up to that number.
In this case, both n and r are 4 (since we are arranging all 4 students), so the formula simplifies to 4!, which is 432*1 = 24.
So, there are 24 different orders in which the program can be arranged.
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