how many ways can you put the fruit in a line

3 identical apples , 4 different bananas , 7 identical cherries



this ones indirect but how do you shade in sets for a venn diagram is it right to left or left to right or all together
like how would I shade this in: (A intersect B intersect c)'

would I do it like this:

((A intersect B ) intersect c)'

or this:

(A intersect (B intersect c))'

or shade in the compliment of the middle of the venn diagram?

This post was edited by brigadier on Mar 8 2014 02:21am

I got an idea...

for the moment lets pretend all the fruit is the same (all apples are apples, all bananas are bananas, ect)

given any string of fruit like "aabbcc", you can get the possible ways to line them up by

n!/(a!b!c!) where n = number of fruits in the line, a = number of apples, etc

so for "aabbcc" we get
6!/(2!2!2!) = 90

so for "aaabbbbccccccc" (which is ALMOST the problem you are working on) we get

14!/(3!4!7!) = X

now we just need to fudge in the fact the bananas are not the same..... if you think about it...each of those X ways has 4 bananas in it..... how many different ways are their to distribute those 4 bananas? 4! ways....

so each of the X ways above actually contains 4! ways "inside it"...

(14!4!)/(3!4!7!) = 14!/(3!7!)

Well I'm not going to bet my life this is correct, but it is what I thought of... hope it helps

I've never been very good at counting, so take this answer as you will.

I'm sure there's a genera formula for something like this, but I would just place things one by one.

So,

First, place the apples: There are (14 choose 3) ways
Then, place the cherries: There are (11 choose 7) ways

Then, arrange the bananas. Because the bananas are different from one another, order will matter: There are (4!) ways of arranging the bananas.

The total number of arrangements would be (14 choose 3) * (11 choose 7) * 4!