Distributing 3 Pears & 4 Apples to 9 People: Combinations

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AI Thread Summary
The discussion revolves around distributing 3 pears and 4 apples among 9 people, with the stipulation that no individual can receive more than one piece of fruit. Participants debate the interpretation of the distribution rules, particularly whether a person can receive one of each type of fruit. Clarifications suggest that each person can only receive either one fruit or none, leading to a more complex combinatorial problem. The final consensus points toward using the formula 9!/(2!3!4!) to calculate the number of ways to distribute the fruits under the given conditions. The conversation highlights the nuances in interpreting distribution rules in combinatorial problems.
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Homework Statement


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?


The Attempt at a Solution


(9,7)[(7,3)-(6!/4!+5!/3!)] where (a,b) represents the 'a choose b' function.
 
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Hi tgt! :smile:
tgt said:
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?

urgh!

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. :wink:
 
tiny-tim said:
Hi tgt! :smile:


urgh!

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. :wink:

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

Are you sure?

You originally quoted:
tgt said:
… no 2 or more fruit is given to the same person*…

which includes "no 2 fruit is given to the same person" …

in other words, one or none each. :confused:
 
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.
 
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?
 

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