distributing money among friends

[galactus]

Here's another counting problem I was wondering about.

how many ways can you distribute $1, $2, $5, $10, and $20 to 5 of your 10 friends. assume that no one gets more than one bill

Wouldn't we just choose 5 of the friends C(10,5) and multiply by 5?.

5*C(10,5)=1260

I bet it's not that easy.

 

[pka]

In this question you are mapping injectively a set of five different items to ten different ‘boxes’. This is a permutation problem: P(10,5).

 

[galactus]

What tripped me up was we are only distributing to 5 out of the 10.

 

[pka]

What tripped me up was we are only distributing to 5 out of the 10.

In many such problems it is best to think of mapping one set to another. In case from a set of five different monetary notes to a set of people, and this must be one to one. We can choose in 10 ways for the $1, in 9 ways for the $2, …, and 6 ways for the $20. That is a permutation of ten taken five at a time.

 

[galactus]

OK, pka, cool. You're always showing me something.