Calculating Number of Distinct x Tuples from a Set A

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SUMMARY

The discussion focuses on calculating the number of distinct x-tuples from a set A, specifically how to determine the number of combinations of 7 tuples from a set of 20 elements. The participants clarify that while the formula for combinations is typically given by \(\frac{n!}{r!(n-r)!}\), this does not account for the order of tuples within the combinations. They conclude that to find the correct number of distinct combinations, one must consider both the selection of pairs and the order of those pairs, leading to the need for additional adjustments to the formula.

PREREQUISITES
  • Understanding of combinatorial mathematics, specifically combinations and permutations.
  • Familiarity with the factorial function and its application in counting problems.
  • Knowledge of tuples and sets, including the distinction between ordered and unordered collections.
  • Basic programming concepts, particularly in Perl, for practical applications of the discussed concepts.
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  • Research the concept of "combinations of combinations" in combinatorial mathematics.
  • Learn about the application of the multinomial coefficient in counting distinct arrangements.
  • Explore programming implementations of combinatorial algorithms in languages like Python or Perl.
  • Study the principles of graph theory as they relate to combinations and permutations.
USEFUL FOR

Mathematicians, computer scientists, and anyone involved in algorithm design or combinatorial optimization will benefit from this discussion, particularly those working with data structures that require efficient counting of distinct arrangements.

  • #31
BicycleTree, you are not allowed to swap a key that has already been swapped.

This is what is meant when he said:

Think of it as a physical system containing 10 physical elements, if 1 is used in one pair, it can't be reused in another pair or again in the same pair.
so, (2, 2) can't be used and (2, 3), (2, 4) can't be used.
 
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  • #32
Yeah, but that doesn't strictly apply to the keyboard example. It's not really important.
 

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