Question 425928
b = bananas
p = pears
o = oranges


mother has 3b + 2p + 2o


how many different ways can she serve these fruits in one week?


i believe your answer will be 7! / (3! * 2! * 2!) = 210


these are permutations because order is important.


a simple example can be used to show you how this works.


suppose it was only 3 days and you had 2b and 1p


the number of ways would be 3! / (2! * 1!) = 3.


those ways would be:


bba
bab
abb


the first column is the first day, the second column is the second day, the third column is the third day.


a sightly more complex example would be:


2b + 2p over 4 days


answer would be 4! / (2! * 2!) = 6


those ways would be:

bbpp
bpbp
bppb
pbbp
pbpb
ppbb


an even more complex example would be:


2b + 2p + 1o in 5 days.


number of ways would be 5! / (2! * 2! * 1!) = 30


these would be:


bbppo
bbpop
bbopp


bpbpo
bpbop
bppbo
bppob
bpobp
bpopb


pbbpo
pbbop
pbpob
pbpbo
pbopb
pbobp


ppbbo
ppbob
ppobb


obbpp
obpbp
obppb


bobpp
bopbp
boppb


opbbp
opbpb
oppbb


pobbp
pobpb
popbb


it gets harder to show you when the numbers get higher.


trust me on 7! / (3! * 2! * 2!)