Question

The 10 students on the Deca Team were trying to decide in what order they should

sit on the bench during the session. In how many different ways can they arrange
themselves from left (next to the coach) to right at the end of the bench)?

Answer 1

3628800

Explanation:

10 students were trying to decide in how many ways they can arrange themselves from left to right.

There are 10 spaces and 10 students are to be sit.

Let us think of the first student.

10 empty spaces are there, so first student has 10 options.

Now, there are 9 empty spaces, so second student has 9 options.

Now, there are 8 empty spaces, so third student has 8 options.

Now, there are 7 empty spaces, so fourth student has 7 options.

:

:

Last student will have only 1 option.

So total number of ways
`= 10 * 9 * 8 * 7 * .....* 1 = 3628800`

OR

Simply we can use the formula:

Number of ways to arrange n persons in a straight line =
`n!` =
`10! = 3628800`