67. In Problem 66, suppose that the coin is tossed a times. Let X denote the number of heads that occur. Show that

$$P(X = i) = \frac{n!}{i!(n-i)!}p^i(1-p)^{(n-i)},$$

i = 0, 1, ..., n HINT: Make use of the fact that

$$\int_0^1 x^{a-1}(1-x)^{b-1} dx = \frac{(a-1)!(b-1)!}{(a+b-1)!},$$

when a and b are positive integers.