Find all combinations of 6 items. Any order, no repeats.

  • Context: Undergrad 
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    Combinations
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Discussion Overview

The discussion revolves around finding the number of combinations of 6 distinct items, specifically focusing on combinations where order does not matter and items cannot repeat. Participants explore different approaches to derive a formula for calculating these combinations.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant expresses a desire for a formula to calculate the combinations of 6 items, acknowledging a lack of recent experience with such problems.
  • Another participant outlines the number of combinations for selecting 1 to 6 items using binomial coefficients, providing specific calculations for each case.
  • A different approach is suggested, where a participant notes that since each item can either be included or not, there are 2^6 total possibilities, and subtracting 1 accounts for the empty set, leading to the solution of 2^6 - 1.
  • A participant reflects on their background in math and relates the problem to a real-life scenario involving creating images for a client, indicating they may have overlooked some combinations.

Areas of Agreement / Disagreement

Participants present multiple methods for calculating combinations, with no consensus on a single approach. The discussion remains open with various interpretations of the problem.

Contextual Notes

Some assumptions about the definitions of combinations and the treatment of the empty set are present, but these are not fully resolved within the discussion.

Who May Find This Useful

Individuals interested in combinatorial mathematics, particularly those looking for different methods to calculate combinations without repetition.

Xzavios
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This may be simple but I want to see a formula and admit I've been out of school too long to figure this one out. Although it's bugging me! I would like to see a formula, too, not just the answer.

So you have 6 items. For example ABCDEF.
You must use at least one item.
Order does not matter (ie. ABC=ACB)
They can not repeat.

So how many different combinations can I create with these items?

Thanks in advanced!
 
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1 item - 6, 2 items - 6x5/2, 3 items - 6x5x4/(3x2), 4 items - same as 2, 5 items - same as 1, 6 items - 1.

It is basically binomial coefficients.
 
If you don't care to break out the number of combinations based on the number of items in each group (as done by mathman), it's even simpler. Each item either is or is not included, so there are 2^6 possibilities. But you want at least one item in each selection, so subtract 1 to account for the empty set. Solution: 2^6 - 1.
 
Thanks guys I knew it was something so simple. As a designer I don't use math much anymore although it was always one of my favorite subjects in school.

This is great because this was based on a real life situation of creating images of these groups for a client. I created 60 so I see now that I'm missing 3.
 

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