Question 887579: in how many ways can nine people be seated on a bench if only three seats are available
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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