What is the probability that of 5 people hired, 2 are from New Jersey? A company in New Jersey is hiring $5$ people for a position. Of the applicants, $7$ are from New Jersey, $8$ are from New York, and $5$ are from Pennsylvania. What is the probability that of the $5$ people hired, exactly $two$ are from New Jersey? I'm not sure how to approach this problem.

Let $A=7$ be the number of applicants from NJ, and $B = 13$ be the number of non NJ applicants. Then the number of ways to choose $2$ persons from NJ is $$\binom{7}{2}$$ The number of ways to choose the rest (non NJ) is $$\binom{13}{3}$$ The total you gave is right, so the probability of interest is $$\frac{\binom{7}{2}\binom{13}{3}}{\binom{20}{5}} = \frac{1001}{2584} = 0.38738390.$$