7 females, and 5 males including Larry.

There are 4 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.

1. Ways to choose Lar, 1F, 2 other M} = 1 C (7,1) C (4,2) = 42

Ways to choose {Lar, 2F, 1 other M}; = 1 C (7,2) C (4,1) = 84

Ways to choose {Lar, 3F, 0 other M} = 1 C (7,3) C (4,0) = 35

Ways to choose 4 from 12 is C (12,4) = 495 P (L and at least 1F) = [42 + 84 + 35] / 495 = 161/495 =.325 approx

2. P (Larry and at least 1 F)

P (at least 1F) = 1 - P (0F) = 1 - { [C (7,0) C (5,4) ] } / C (12,4) = 5/495 = 490/495 = 98/99 =.99.

Ways to choose Larry = 1 C (1,1) = 1 P (Larry and at least 1 F) = 1 (98/99) = 98/99 =.99 approx