Question 887579
this should be 9P3 = 9*8*7 = 504


make it simpler and you can see how it works.


assume 4 people for 3 seats.


number of ways would be 4P3 = 4*3*2 = 24


let the people be a,b,c,d


number of possible combinations where order doesn't matter would be 4C3 = 4.


those combinations are:

abc
abd
acd
bcd


each one of these combinations can be arranged in 6 ways.


abc arrangements would be:


abc
acb
bac
bca
cab
cba


abd arrangements would be:


abd
adb
bad
bda
dab
dba


acd arrangements would be:


acd
adc
cad
cda
dac
dca


bcd arrangements would be:


bcd
bdc
cbd
cdb
dbc
dcb 


total possible arrangements are 4 * 6 = 24


the formula to use is 4P3 in this example.


note that 4P3 = 4C3 * 3! which means you got 4 possible combinations * 6 possible arrangements for each combination to get 24 possible permutations.


the same permutation formula is applied when n = 9 to get 9P3 which is equal to 504.