Chapter 9.1, Problem 30E

Solution

To state: The number of sequence of head and tail that has exactly seven head if a coin is tossed 20 times.

The resultant sequences are $77,520$ .

Given information:

It is given that a coin is tossed 20 times.

Explanation:

Consider the given information,

A coin is tossed 20 times.

The formula of finding number of possible sequences of selecting r object from the set of n without repetition is given by:

  $C{}_r=\frac{n!}{r!\left(n-r\right)!}$

The number of possible sequence of heads and tails that have exactly 7 heads in the 20 tosses of a coin is:

  $\begin{array}{c}C{}_7=\frac{20!}{7!\left(20-7\right)!}\\ =\frac{20!}{7!13!}\\ =\frac{20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13!}{\left(7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\right)13!}\\ =\frac{390700800}{5040}\\ =77,520\end{array}$

Therefore, the possible sequence of head and tails that have exactly seven heads if the coin is tossed 20 times is $77,520$ .