Chapter 13.2, Problem 6AYU

$C\left(n,r\right)=$ _______________________.

To determine

To fill: $C(n,r)=$ _____

Answer to Problem 6AYU

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

Explanation of Solution

Given:

$C(n,r)$

Calculation:

$C(n,r)$ is the combination of $n$ objects chosen from $r$ Distinct objects without repetition.

The number of arrangements of $n$ objects using $r\le n$ of them, in which

1. The $n$ objects are distinct,

2. Once an object is used, it cannot be repeated, and

3. Order is not important,

is given by the formula

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