Question

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. find the probability that
a. comic d will perform first.
b. comic c will perform first and comic e will perform fifth.
c. the comedians will perform in the following order: d, c, e, b, f, a
d. comic f or comic a will perform fifth.
a.
(type a fraction. simplify your answer)

Explanation:

Step1: Calculate total number of permutations

The total number of ways to arrange \(n = 6\) comics is \(n!=\ 6! = 6\times5\times4\times3\times2\times1=720\)

Step2: Calculate probability for part a

For comic \(D\) to perform first, the remaining \(5\) comics can be arranged in \(5! = 5\times4\times3\times2\times1 = 120\) ways.
The probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{5!}{6!}\)
Since \(6! = 6\times5!\), then \(P=\frac{5!}{6\times5!}=\frac{1}{6}\)

Answer:

\(\frac{1}{6}\)