Calculating Number of Distinct x Tuples from a Set A

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The discussion focuses on calculating the number of distinct x-tuples that can be formed from a set A, specifically when creating combinations of 7 tuples from a set of 20 elements. Participants clarify the difference between tuples and sets, emphasizing that the order of elements matters in tuples but not in sets. The correct approach involves using combinations to select pairs while accounting for the distinctness of elements across the pairs. The formula discussed is a combination of factorial calculations, where the order of the pairs and the distinctness of elements must be considered. Ultimately, the conversation highlights the complexity of counting distinct tuples while ensuring no element is reused across pairs.
  • #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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