Probability precalculus word problem

Question

A law office interviews paralegals for 10 openings. There are 15 paralegals with two years of experience and 19 paralegals with one year of experience. How many combinations of six paralegals with two years of experience and four paralegals with one year of experience are possible?

Answer 1

First we find how many combinations of 6 out of 15 and 4 out of 19 we can make.

₁₅C₆ = 5005

₁₉C₄ = 3876.

Then we multiply those two values together using the counting principle.

5005 x 3876 = 19,399,380