Chapter 9, Problem 18E

When two fair coins are tossed the probability of tossing two heads is $\frac{1}{4}$; when three fair coins are tossed the probability of tossing two heads and one tail is $\frac{3}{8}$; when four fair coins are tossed the probability of tossing two heads and two tails is $\frac{6}{16}$; when five fair coins are tossed the probability of tossing two heads and three tails is $\frac{10}{32}$. Using the sequence $\frac{1}{4},\frac{3}{8},\frac{6}{16},\frac{10}{32},\mathrm{...}$ as your guide,

a. determine the probability of tossing two heads and four tails when six fair coins are tossed.

b. determine the probability of tossing two heads and 10 tails when 12 fair coins are tossed. (Hint: Find an explicit formula first.)