Assume that there are 15 board members: 9 females, and 6 males including Carl. There are 3 tasks to be assigned. Note that assigning the same people different tasks constitutes a different assignment.

Question

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

Answer 1

p(Carl) = 1/15
assuming Carl is male, that still leaves 9 females out of the 14 people left.
So, P(Carl,female) = 1/15 * 9/14
And there 3P2 ways that she and Carl can be assigned tasks.