Permutations/You have 12 postcards to send to 5 friends ...

Quote:

Originally Posted by jlt1209

You have twelve different postcards that you want to send to five friends.
a) If each friend can receive any number of postcards, and all the cards must be sent, in how many ways can this be done?

b) If each friend must receive at least 1 postcard, and all cards must be sent, in how many ways can this be done?

a) You count the number of functions from a set of twelve to a set of five.

b) You must count the number of surjections from a set of twelve to a set of five.
$Surj(12,5) = \sum\limits_{k = 0}^5 {\left( { - 1} \right)^k {{5} \choose {k}}\left( {5 - k} \right)^{12} }$