involving the assignment of tasks to student union board members. Assume that there are 12 board members: 7 females, and 5 males including Larry. There are 3 tasks to be assigned.

Question

involving the assignment of tasks to student union board members. Assume that there are 12 board members: 7 females, and 5 males including Larry. There are 3 tasks to be assigned. Note that assigning the same people different tasks constitutes a different assignment.

(1) Find the probability that both males and females are given a task. 

 

(2) Find the probability that Larry and at least one female are given tasks. 

Answer 1

1) This is 1 - P(all females) - P(all males) =

1 - C(7,3)/C(12,3) - C(5,3)/C(12,3) = 1 - 35/220 - 10/220 = 35/44

2) P(Larry and 1 female and 1 other male) + P(Larry and 2 females) =

C(7,1)C(4,1)/C(12,3) + C(7,2)/C(12,3) =

28/220 + 21/220 = 49/220