Chapter 12.6, Problem 28PPE

To determine

To calculate: The value of expression $C{}_4$ .

Answer to Problem 28PPE

The value is $5$ .

Explanation of Solution

Given information:

  $C{}_4$

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 ,

  $C{}_4$

  $\begin{array}{l}C{}_4=\frac{5!}{4!\left(5-4\right)!}\\ =\frac{5!}{4!1!}\\ =\frac{5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1\times 1}\\ =5\end{array}$

Hence, the value is $5$ .