Problema Solution
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 fifth.
b. Comic A will perform fifth and Comic C will perform fourth.
c. The comedians will perform in the following order: D, A, C, E, B, F.
d. Comic B or Comic F will perform third.
-type fractions in a simplified form-
Answer provided by our tutors
a.Comic D will perform 5th.
# of ways to succeed: 1*5!
# of possible outcomes: 6!
P(D is 5th) = 5!/6!
P(D is 5th) = 1/6
b. Comic A will perform fifth and Comic C will perform fourth.
# of ways to succeed: 1*1*4! = 4!
P(A will perform 5th and C will perform 4th) = 4!/6!
P(A will perform 5th and C will perform 4th) = 1/30
c. The comedians will perform in the following order: D, A, C, E, B, F.
P(D, A, C, E, B, F) = 1/6!
P(D, A, C, E, B, F) = 1/720
d. Comic B or Comic F will perform third.
# of ways to succeed: 2!*4!
P(Comic B or Comic F will perform 3rd) = 2!*4!/6!
P(Comic B or Comic F will perform 3rd) = 1/15