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. \\( \frac { 1 } { 6 } \\) (type a fraction. simplify your answer.)
b. \\( \frac { 1 } { 30 } \\) (type a fraction simplify your answer )
c. (type a fraction simplify your answer )

Explanation:

Step1: Calculate total number of permutations

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 6\), so the total number of ways the 6 comics can perform is \(n!=6! = 6\times5\times4\times3\times2\times 1=720\)

Step2: Calculate probability for part c

There is only 1 way for the comedians to perform in the order \(D,C,E,B,F,A\). Using the probability formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), the probability \(P=\frac{1}{720}\)

Answer:

\(\frac{1}{720}\)