Chapter 13.1, Problem 42E

To determine

To calculate: The number of different ways to form a 12-member juries.

Answer to Problem 42E

The number of different ways to form a 12-member juriesare $18564$ .

Explanation of Solution

Given information:

There are 18 people in a group to choose in order to make 12-member juries.

Formula used:

If there are n objects taken r at a time then combination is defined as $C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$ .

Calculation:

Consider the provided information that there are 18 people in a group to choose in order to make 12-member juries.

In order to make different 12-member juries, use combination as selection does not matter.

Recall that if there are n objects taken r at a time then combination is defined as $C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$ .

Here n is 18 and r is 12for $C\left(18,12\right)$ .

  $\begin{array}{c}C\left(18,12\right)=\frac{18!}{12!\left(18-12\right)!}\\ =\frac{18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\cdot 12!}{12!\cdot 6!}\\ =\frac{18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13}{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}\\ =18564\end{array}$

Thus, the number of different ways to form a 12-member juries are $18564$ .