Question

$C(n,r)=\_\_\_\_\_\_$

Short answer

The complete statement is$C(n,r)=\frac{n!}{(n-r)!r!}$.

Step-by-step solution

Step 1. Given information.

The given statement is:

$C(n,r)=\_\_\_\_\_\_\_$

Step 2. Determine the value for the blank. 

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

• The $n$objects are distinct
• Once an object is used, it cannot be repeated,
• Order is not important.

is given by the formula:

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

Step 3. Conclusion.

The complete statement is$C(n,r)=\frac{n!}{(n-r)!r!}$.