SOLUTION: There are 6 people running the 100 meter dash. How many different orders can the runners finish?

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Question 275509: There are 6 people running the 100 meter dash. How many different orders can the runners finish?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
6! = 6*5*4*3*2*1 = 720 possible ways.

assume it was only 3 people.

that would be 3! = 3*2*1 = 6

let the people be abc.

order of finish possible would be:

abc
acb
bac
bca
cab
cba

this is called a permutation because order is important.

assume it was 4 people.

number of ways would be 4! = 4*3*2*1 = 24

possible ways get a lot bigger after 4.

assume the people were abcd

possible ways would be:

abcd
abdc
acbd
acdb
adbc
adcb
bacd
badc
bcad
bcda
bdac
bdca
cabd
cadb
cbad
cbda
cdab
cdba
dabc
dacb
dbac
dbca
dcab
dcba