In how many ways can 10 people stand in a line?

1 Answer

#10! = 3,628,800#

Explanation:

Assuming they are all in one line, we can line them up in #10!# ways: there are 10 people who can stand in position 1, then 9 remaining who can stand in position 2, then 8 remaining who can stand in position 3, etc.

#10xx9xx8xx7xx6xx5xx4xx3xx2xx1=10! = 3,628,800#

If we add the ability to move the 10 places where people can stand, then we'll have to multiply #10!# by some number that describes the number of allowable ways to place standing spots.