Combination or Permutation Calculation

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Discussion Overview

The discussion revolves around calculating the number of distinct subsets that can be formed from the numbers 1 through 6, specifically focusing on subsets that must include the number 2. The problem involves combinatorial reasoning and touches on the distinction between combinations and permutations.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant presents a problem of selecting 4 items from the numbers 1 to 6, emphasizing the requirement that the number 2 must be included in each subset.
  • Another participant suggests that by choosing the number 2 first, the problem simplifies to selecting 3 additional numbers from the remaining 5.
  • A later reply confirms the simplification by stating that a tree diagram was used to arrive at the same conclusion.
  • Terminology is discussed, with a participant clarifying that the term "distinct" should be replaced with "order doesn't count" to accurately describe the nature of combinations versus permutations.

Areas of Agreement / Disagreement

Participants generally agree on the approach to the problem and the terminology used, but there is no explicit consensus on the final calculation or the specific method to be used.

Contextual Notes

The discussion does not resolve the exact number of distinct subsets, and the implications of using a tree diagram versus a formula remain unaddressed.

Who May Find This Useful

Individuals interested in combinatorial mathematics, particularly those dealing with problems involving selections and the distinction between combinations and permutations.

Vector1962
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TL;DR
How to calculate subsets of 4 items from a set of 6 items and only count the subsets that have a specific item.
Hello Forum:
I have numbers 1 through 6 from which i must select 4 items. The twist is that i need to count only those subsets that include the number 2 all of the subsets are 'distinct' --> 2145 is the same as 2415. My quick calculation yields 15 distinct subsets however some of those do not contain the number 2. is there a formula to use or will i have to make some kind of tree diagram to list them? thanks in advance for the help. also, i picked intermediate but it may be a pretty basic question.
 
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Choose the number 2. Then the problem reduces to selecting any 3 from 5 numbers.
 
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Excellent... thank you. for what it's worth and for the number of items involved i made the tree diagram and arrive at exactly what you suggest.
 
Just a word about terminology before leaving this. Instead of saying " all of the subsets are 'distinct' --> 2145 is the same as 2415. ", you should say that order doesn't count. Those are the magic words that we look for to determine that it is a problem about the number of combinations. If order counts (2145 not the same as 2415), then it is a problem about the number of permutations.
 

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