Question

fill in the blanks.
six stand - up comics, a, b, c, d, e, and f, are to perform on a single evening at a comedy club. the order of performance is determined by random selection. the probability that comic e will perform first is the number of ____ with comic e performing first divided by ____.

six stand - up comics, a, b, c, d, e, and f, are to perform on a single evening at a comedy club. the order of performance is determined by random selection. the probability that comic e will perform first is the number of with comic e performing first divided by

Explanation:

Step1: Recall the formula for probability

The probability \(P(A)\) of an event \(A\) is given by \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of elements in the event \(A\) and \(n(S)\) is the number of elements in the sample space \(S\).

Step2: Interpret the problem in terms of permutations

The number of permutations of \(n\) distinct objects is \(n!\). Here, if comic \(E\) performs first, then we need to permute the remaining \(n - 1=5\) comics. The number of permutations of the remaining \(5\) comics is \(5!\) (this is \(n(A)\), the number of favorable outcomes). The total number of permutations of \(6\) comics is \(6!\) (this is \(n(S)\), the number of elements in the sample space).

Answer:

The probability that comic \(E\) will perform first is the number of \(\boldsymbol{5!}\) (permutations of the remaining \(5\) comics) with comic \(E\) performing first divided by \(\boldsymbol{6!}\) (total permutations of \(6\) comics).