# Homework Help: Distributing objects

1. Nov 17, 2008

### tgt

1. The problem statement, all variables and given/known data
If we like to distribute 3 pears and 4 apples to 9 people such that no 2 or more fruit is given to the same person, in how many ways can this be done?

3. The attempt at a solution
(9,7)[(7,3)-(6!/4!+5!/3!)] where (a,b) represents the 'a choose b' function.

2. Nov 18, 2008

### tiny-tim

Hi tgt!
urgh! :yuck:

Hint: let's rewrite the question …

we want to distribute 3 pears and 4 apples and 2 nothings to 9 people so that they get one each.

3. Nov 18, 2008

### tgt

No. A person is allowed to have two pieces of fruit such as one pear and one apple.

4. Nov 18, 2008

### tiny-tim

Are you sure?

You originally quoted:
which includes "no 2 fruit is given to the same person" …

in other words, one or none each.

5. Nov 18, 2008

### HallsofIvy

tiny-tim, I would interpret "no 2 or more fruit" as meaning each person gets either 0 or 1 fruit of any kind- so "one pear and one apple" wou.ld violate that. And I would interpret "A gets an apple" as different from "A gets a pear". That's a noticeably harder problem.

6. Nov 18, 2008

### tgt

It seems both HallsoIvy and tiny tim are correct. In which case the answer is 9!/(2!3!4!)

But that's not a noticeable hard problem, hallsofivy?