(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?
(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.
(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
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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.