SOLUTION: I have a probability problem. If someone can help me figure out the steps and answer, it would be great. Thank you! problem: If a mother has three bananas, two pears and two

Question 425928: I have a probability problem. If someone can help me figure out the steps and answer, it would be great. Thank you!
problem:
If a mother has three bananas, two pears and two oranges, in how many different ways can she give the fruit to her daughter in one week, one piece of fruit per day?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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!)

RELATED QUESTIONS
I have had a hard time trying to figure out this problem: Its a right triangle with a... (answered by ankor@dixie-net.com)

hi i need help with the following problem: the cubed root of 2x+7=5 (the five is not... (answered by ewatrrr)

I have attempted this problem about 6 times now, and I always get stuck :( I'm supposed... (answered by rfer)

Happy Wednesday all, I would like to request some help with the problem I have listed (answered by HasanSahin)

I am having a very hard time proving this identity sin 2x + sin 4x/cos 2x - cos 4x =... (answered by TakeATuition.com)

I need help with this problem, i believe i have the right answer but i need someone to... (answered by josgarithmetic)

okay... welcome to my nightmear! The perimeter of a triangle is 33 centimeters. The... (answered by longjonsilver)

I have been struggling to figure out this math problem and I was wondering if someone... (answered by monika_p)

I have been struggling to figure out this math problem and I was wondering if someone... (answered by Fombitz)