There are 20 students competing to be on the Math Team. Thirteen of them specialize in algebra,

Question:

There are 20 students competing to be on the Math Team. Thirteen of them specialize in algebra, 4 of them specialize in geometry, and 3 of them specialize in calculus. Only 5 spots on the team are available, and team members will be chosen at random, regardless of specialty. Let X be the number of calculus specialists who make the team.
a. Find the probability mass function for the number of math team members who are calculus specialists.
b. Find the cumulative function for the number of math team members who are calculus specialists.
c. What is the expected number of calculus specialists who make the team?
d. What is the variance of the number of calculus specialists who make the team? Distribution
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