Question

there are 9 performers who will present their comedy acts this weekend at a comedy club. one of the performers insists on being the last stand - up comic of the evening. if this performer’s request is granted, how many different ways are there to schedule the appearances? (type a whole number.)

Explanation:

Step1: Fix the last performer

Since one performer must be last, we only need to arrange the remaining \(9 - 1=8\) performers.

Step2: Calculate the number of permutations

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 8\), and the formula for permutations of \(n\) objects is \(P(n,n)=\frac{n!}{(n - n)!}=n!\) (because \(0!=1\)). So the number of ways to arrange \(8\) performers is \(8! = 8\times7\times6\times5\times4\times3\times2\times1\).

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Answer:

\(40320\)