Chapter 12.6, Problem 35PPE

To determine

To calculate: The value of expression $C{}_9$ .

Answer to Problem 35PPE

The value is $10$ .

Explanation of Solution

Given information:

  $C{}_9$

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:

Consider ,

  $C{}_9$

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

Hence, the value is $10$ .