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I have 8 pieces of strawberry candy (all identical) and 7 pieces of rhubarb candy (all identical). Find the number of ways I can distribute this candy to 4 children.

 

Thanks in advance to whoever answers! and please please explain fully! Please do not just give me an answer, since I wouldn't know how you got it. Anyways, thanks!

 Aug 9, 2020
 #1
avatar+110686 
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I have 8 pieces of strawberry candy (all identical) and 7 pieces of rhubarb candy (all identical). Find the number of ways I can distribute this candy to 4 children.

Are the 4 children all identical? I will assume not.

I will also assume that 1 or more children could get nothing.

 

Say you put the strawberries in a line.  You put one child at the front of the line.   Now you insert the other 3 children somewhere in the line.

Each child gets the strawberries that are between them and the next child.

The first child is set

So we need to know how many variations there are with 3 children and 8 strawberries.  That is 11C3 = 11C8 = 165

(this is called stars and bars method)

For the rhubarbs it is    10C3 =  10C7 = 120

 

Put them together and you get 120*165 = 19800  ways.

 Aug 10, 2020
 #2
avatar+359 
+3

Thank you!!!! Very well explained and I now know how to do it well!

iamhappy  Aug 10, 2020
 #3
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That is great :)

Melody  Aug 11, 2020

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