A new movie is opening and 10 people arrive at the same time to the theatre and make a mad dash for the ticket line. How many ways could the 10 people line up?

Question

Algebra 2b test review question

Answer 1

Hi Aries, let's figure this out!

 

You have ten places in line to fill:

 

_, _, _, _, _, _, _, _, _, _

 

When deciding which person will fill the first spot, you have ten people from which to choose. Once that person is placed, there are only nine left from which to choose, and so on....

 

10, 9, 8, 7, 6, 5, 4, 3, 2, 1.

 

To find the solution, multiply all these numbers together.

 

(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) = 10! , which is called 10 factorial, = 3,628,800 ways those 10 people could line up.

Answer 2

This is a combination:

10!

362,880,000