SOLUTION: a certain number of friends are waiting in line to board a new roller coaster. They can board the ride in 5,040 diffrent ways. How many friends are in line

Question 967412: a certain number of friends are waiting in line to board a new roller coaster. They can board the ride in 5,040 diffrent ways. How many friends are in line

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i don't know if there's a formula to find this.
you can try several numbers and iterate to get the answer.
the number of friends will be x, where x! = 5040.
try 5! to get 120
try 6! to get 720
try 12! to get 479001600 which is way too big.
try 9! to get 3628880 which is still too big.
it whould be 7 or 8.
try 7! to get 720 * 7 = 5040.

the number is 7 because 7! = 5040.

the easy way was to work up.

1! = 1
2! = 2
3! = 2! * 3 = 2*3 = 6
4! = 3! * 4 = 6 * 4 = 24
5! = 4! * 5 = 24 * 5 = 120
6! = 5! * 6 = 120 * 6 = 720
7! = 6! * 7 = 720 * 7 = 5040

you did have to know that the number of different arrangements of x people is x!.

but once you knew that, the rest was just working through the numbers.

a calculator that does factorials is helpful.

it takes the drudgery out of the calculations.

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