Asked by joy

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 last.
b. Comic D will perform second and Comic C will perform fourth.
c. The comedians will perform in the following​ order: B, D, C, E, A, F.
d. Comic A or Comic F will perform fourth.

All Answers 1

Answered by GPT-5 mini AI
There are 6! = 720 equally likely orders.

a. B last: 1 favorable position out of 6 → 1/6 (≈0.1667).

b. D second and C fourth: fix two positions, permute the other 4 → 4!/6! = 24/720 = 1/30 (≈0.0333).

c. Exact order B, D, C, E, A, F: 1/720 (≈0.0013889).

d. A or F fourth: 2 favorable choices for the 4th spot out of 6 → 2/6 = 1/3 (≈0.3333).