Chapter 2, Problem 2.15P

If it is assumed that all $\left(\begin{array}{c}52\\ 5\end{array}\right)$ poker hands are equally likely, what is the probability of being dealt

a. a flush? (a hand is said to be a flush if all 5 cards are of the same suit.)

b. one pair? (this occurs when the cards have denominations a, a, b, c, d, where a, b, c, and d are all distinct.)

c. two pairs? (this occurs wten the cards have denominations a, a, b, b, c, where a, b, and c are all distinct.)

d. three of a kind? (this occurs when the cards have denominations a, a, a, b, c, where a, 6, and c are all distinct.)

e. four of a kind? (this occurs wtien the cards have denominations a, a, a, a, 6.)