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

• September 24th 2008, 03:32 PM
jlt1209
Permutations/You have 12 postcards to send to 5 friends ...
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?

• September 24th 2008, 03:58 PM
Plato
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.
$Surj(12,5) = \sum\limits_{k = 0}^5 {\left( { - 1} \right)^k {{5} \choose {k}}\left( {5 - k} \right)^{12} }$