(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?

Guest Jan 14, 2020

#1**0 **

(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.

Guest Jan 14, 2020

#2**+1 **

(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.

Melody Jan 16, 2020