Question: A task force working to preserve the nose of Saint Tabascus is forming a chemistry committee with five members. They have calculated that there are 65,780 ways to form this committee. Of these, 24,480 have exactly one woman, 22,848 have exactly two women, 8,568 have exactly three women, 1,260 have exactly four women, and 56 have exactly five women.
(a) How many committees have at least three women?
(b) How many committees have no women?
(c) How many committees have at most two women?
(d) Challenge: How many members does the Preserve the Nose of Saint Tabascus Task Force have? And how many of those are women?