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 B will perform fourth.
b. Comic $\mathrm{C}$ will perform last and Comic $\mathrm{E}$ will perform third.
c. The comedians will perform in the following order: B, C, E, D, A, F.
d. Comic A or Comic F will perform last.
a

Step 1 ：The total number of ways the comics can perform is 6!, which is the number of permutations of 6 distinct items.

Step 2 ：For comic B to perform fourth, we need to consider the number of ways the other 5 comics can perform in the remaining 5 spots. This is 5!, which is the number of permutations of 5 distinct items.

Step 3 ：The probability is then the number of favorable outcomes (5!) divided by the total number of outcomes (6!).

Step 4 ：Calculate the total number of outcomes: \(6! = 720\)

Step 5 ：Calculate the number of favorable outcomes: \(5! = 120\)

Step 6 ：Calculate the probability: \(\frac{120}{720} = 0.16666666666666666\)

Step 7 ：Final Answer: The probability that Comic B will perform fourth is \(\boxed{0.16666666666666666}\)