c) Show that P(A

_{i} Intersection A

_{j} intersection A

_{k}) = 1!/4!

d) Show that the probability of at least one match is P (A

_{1} U A

_{2} U A

_{3} U A

_{4}) = 1 - 1/2! + 1/3! - 1/4!

e) Extend this exercise so that there are n balls in the urn. Show that the probability of at least one match is:

P(A

_{1 }U A

_{2} U...U A

_{n}) = 1 - 1/2! + 1/3! - 1/4! +...+

__(-1)__^{n+1 }= 1 - (1- 1/1! + 1/2! - 1/3! +...+

__(-1)__^{n} ).

n! n!

This is exercise 1.4-19 from Probability and Statistical Inference, Hogg and Tanis 8th edition. If anyone could help me with this problem I would greatly appreciate it.