Chapter 9, Problem 91RE

To determine

To find: numbers of ways a jury of 12 people can be selected

Answer to Problem 91RE

The numbers of ways a jury of 12 people can be selected are 4515856800

Explanation of Solution

Given:

A group of potential jurors that has been narrowed down to 32 people

32 people in jury

Consider a group of potential jurors that has been narrowed down to 32 people

Note that there are 32 people in jury and 12 people has to be selected.

In selection order is not important.

So use combination formula to get

  $\begin{array}{l}C{}_{12}=\frac{32!}{12!(32-12)!}\hfill \\ =\frac{32!}{12!20!}\hfill \\ =\frac{32\times 31\times 30\times 29\times 28\times 27\times 26\times 25\times 24\times 23\times 22\times 21\times 20!}{\left(12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\right)\times 20!}\hfill \\ =4515856800\hfill \end{array}$

The numbers of ways a jury of 12 people can be selected are 4515856800