7females, 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

It equals 1373.5 that’s the solution