In how many ways i can put two three things in two bags

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Discussion Overview

The discussion revolves around the problem of determining the number of ways to place two fruits into two bags, with specific constraints regarding the fruits and the bags. Participants explore various interpretations of the problem, including the distinguishability of the fruits and the arrangement of the bags.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant initially presents the problem with two oranges, one apple, and one banana, seeking to place two of them into two bags, with the assumption that only one fruit can be placed in each bag.
  • Another participant interprets the problem as involving three distinguishable apples and provides a breakdown of possible arrangements, suggesting that if the apples are identical, the number of arrangements changes.
  • Several participants clarify that the two oranges are indistinguishable, emphasizing that order matters in the combinations, and they seek to understand how this affects the total number of arrangements.
  • One participant expresses confusion about the problem's wording and suggests that the task is to select two items from four, noting that this could be approached by listing unique pairs.
  • Another participant highlights the confusion regarding the reposting of the same question and encourages clarity in stating the problem and previous attempts to solve it.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the problem's interpretation or the correct approach to finding the solution. Multiple competing views on how to handle the indistinguishability of the fruits and the arrangement of the bags remain evident.

Contextual Notes

There are limitations in the clarity of the problem statement, particularly regarding the definitions of distinguishability and the arrangement of items. The discussion reflects varying assumptions about the nature of the fruits and the bags.

rajemessage
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Dear all,

I have two oranges,one apple and one banana.
i want to put two of them at a time in two bags having one each.
in how many ways i put them?yours sincerely
 
Last edited:
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Hello, rajemessage!

The instructions are not clear.
I assume my interpretation is correct.

In how many ways i can put three apples in two bags?
Each bag will have at least one apple.
I assume that the three apples are distinguishable
\quadas are the two bags.
Then we have six ways: \;\begin{array}{ccc} |AB|C| & |A|BC| \\ |AC|B| & |B|AC|\\ |BC|A| & |C|AB| \end{array}

If the three apples are identical, we have two ways: \;\begin{array}{cc} |**|*| \\ |*|**| \end{array}

If the two bags are also identical we have one way:
\quadone apple in one bag, two apples in the other.

 
I have two oranges,one apple and one banana.
i want to put two of them at a time in two bags having one(one froot at max in one bag) each.

There are two oranges and they are indistinguisable(they are two but their value is same).
[order does matter for all combination]
bags have positions like first bag will be at first position and second will be at second position and it will not be changed.

so please tel me in how many ways i put them in bags?
yours sincerely
 
how to find combinatin in following situation

I have two oranges,one apple and one banana.
i want to put two of them at a time in two bags having one(one fruit at max in one bag) each.

There are two oranges and they are indistinguishable(they are two but their value is same).
[order does matter for all combination]
bags have positions like first bag will be at first position and second will be at second position and it will not be changed.

so please tel me in how many ways i put them in bags?
yours sincerely
 
rajemessage said:
I have two oranges,one apple and one banana.
i want to put two of them at a time in two bags having one(one fruit at max in one bag) each.

There are two oranges and they are indistinguishable(they are two but their value is same).
[order does matter for all combination]
bags have positions like first bag will be at first position and second will be at second position and it will not be changed.

so please tel me in how many ways i put them in bags?

Hi rajemessage, :)

I'm a little confused by the wording of the problem but as I understand your description, you basically are trying to select two items of out 4 to put into 2 bags. Since only 1 item can be placed in each bag, this is really just choosing two items. We are looking for the number of unique pairs from this group, where order matters.This problem is possible to do by brute force actually since the number of items is small.

A few possible arrangements would be "Orange,apple", "Apple, orange" and "Orange, banana". Can you list the rest?
 
rajemessage said:
I have two oranges,one apple and one banana.
i want to put two of them at a time in two bags having one(one fruit at max in one bag) each.

There are two oranges and they are indistinguishable(they are two but their value is same).
[order does matter for all combination]
bags have positions like first bag will be at first position and second will be at second position and it will not be changed.

so please tel me in how many ways i put them in bags?

yours sincerely

I too am confused, but my confusion lies primarily with the fact that you created a new thread to ask a question you previously asked. (Tmi)

I have merged your two threads, and would ask that in the future you not re-post the same question more than once. Not only is it just downright inefficient to have the same questions posted multiple times, it can also lead to duplication of effort on the part of our helpers, and we value their time greatly and do not want to see it wasted.

As you can see, people are a bit unclear on the actual problem, so I suggest you state the problem exactly as given and show what you have tried so our helpers know where you are stuck and can offer the best help possible. :D
 

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