Distributing 3 Pears & 4 Apples to 9 People: Combinations

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Homework Help Overview

The problem involves distributing 3 pears and 4 apples among 9 people, with the condition that no person receives more than one piece of fruit. The discussion centers around interpreting the constraints of the distribution.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the interpretation of the phrase "no 2 or more fruit is given to the same person," with differing views on whether this allows for a person to receive one of each type of fruit.

Discussion Status

The discussion is ongoing, with participants presenting different interpretations of the problem's constraints. Some have suggested a combinatorial approach based on their understanding of the rules, while others are questioning the assumptions made about how fruit can be distributed.

Contextual Notes

There appears to be confusion regarding the interpretation of the problem statement, particularly concerning the allowance of multiple types of fruit for a single person. This ambiguity is influencing the proposed methods for solving the problem.

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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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