Chapter 8.1, Problem 94E

Committee selection. A $4\text{-person}$ grievance committee is to include employees in $2$ departments, $A$ and $B$, with $15$ and $20$ employees, respectively. If the $4\text{-person}$ are selected at random from the $35$ employees, what is the probability of selecting

(A) $3$ from $A$ and $1$ from $B$ ?

(B) $2$ from $A$ and $2$ from $B$ ?

(C) All $4$ from $A$ ?

(D) At least $3$ from $A$ ?