Question

Notation What does the symbol ! represent? Six different people can stand in a line 6! different ways, so what is the actual number of ways that six people can stand in a line?

Short answer

The symbol “!” after any number represents the product of all non-zero positive integers equal to less than the given number.

The actual number of ways that six different people can stand in a line is equal to 720.

Step-by-step solution

Given information

The number of ways that six different people can stand in a line is equal to 6!.

Meaning of the symbol “!”

The factorial of a number is the product of all the numbers (positive non-zero integers) equal or less than the given number up to 1.

It is represented by the symbol “!”.

Mathematically,

$n!=n\times \left(n-1\right)\times ...\times 1$

 Step 3: Compute the factorial of number 6

It is given that six different people can stand in a line in 6! ways.

The value of 6! is calculated as follows:

$$\begin{gathered} 6!=6\times \left(6-1\right)\times \left(6-2\right)\times ...\times 1 \\ =6\times 5\times 4\times 3\times 2\times 1 \\ =720 \end{gathered}$$

Therefore, the number of ways that six different people can stand in a line is equal to 720.