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(a) While travelling abroad, I bought 7 identical bags of candy for 3 friends. How many ways can I distribute the candy to my 3 friends, so that each friend gets at least one bag of candy?

(b) I also bought 7 different postcards. How many ways can I send the postcards to my 3 friends, so that each friend gets at least one postcard?

 Jan 14, 2020
 #1
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(a) By stars and bars, the number of ways is C(10,3) = 120.

 

(b) By stars and bars, the number of ways is C(13,3) = 286.

 Jan 14, 2020
 #2
avatar+109518 
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(a) While travelling abroad, I bought 7 identical bags of candy for 3 friends. How many ways can I distribute the candy to my 3 friends, so that each friend gets at least one bag of candy?

 

a)  Give each of the friends on bag.

There are 4 bags left to be shared between the 3 friends

   * |* *| *

Using stars and bars I think there are  6C2 = 15 ways

 

(b) I also bought 7 different postcards. How many ways can I send the postcards to my 3 friends, so that each friend gets at least one postcard?

This is much harder.

I'm not sure.

 Jan 16, 2020
 #3
avatar+109518 
+1

(b) I also bought 7 different postcards. How many ways can I send the postcards to my 3 friends, so that each friend gets at least one postcard?

This is much harder.

 

Maybe

(3*7*6)+(6*7*6*5)+2*(3*7*6*5*4)  = 6426

 

It is most likely incorrect.

 Jan 16, 2020
 #4
avatar+109518 
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If/when you know the answers please share them with the forum :)

 Jan 16, 2020

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