Chapter 12.6, Problem 37PPE

To determine

To calculate: The number of combinations of 9 jurors are possible on a 12-person jury.

Answer to Problem 37PPE

There are $220$ combinations.

Explanation of Solution

Given information:

For some civil cases, at least 9 out of 12 jurors must agree on a verdict.

Formula used:

A combination is a selection of objects without regard to order. The expression $C{}_r$ represents the number of combination of $n$ objects chosen $r$ at a time.

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

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

According to the question,

At least 9 out 12 jurors agree on the verdict.

For combinations of 9 jurors out of 12 person jury we follow the combination formula.

  $\begin{array}{l}C{}_9=\frac{12!}{9!\left(12-9\right)!}\\ =\frac{12!}{9!3!}\\ =\frac{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\times 3\times 2\times 1}\end{array}$

  $\begin{array}{l}=\frac{12\times 11\times 10}{3\times 2\times 1}\\ =4\times 11\times 5\\ =220\end{array}$

Hence, there are $220$ combinations of 9 jurors that are possible on a 12- person jury.