SOLUTION: in how many ways can nine people be seated on a bench if only three seats are available

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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