How do I get the total number of unique pairs of a set in the database

Question

4 items   A B C D   6 unique pairs possible   AB AC AD BC BD CD   What if I have 100 starting items  How many unique pairs are there  Is there a formula I can throw this into

User · Answer

TLDR  The formula is n n-1  2 where n is the number of items in the set   Explanation   To find the number of unique pairs in a set  where the pairs are subject to the commutative property  AB   BA   you can calculate the summation of 1   2          n-1  where n is the number of items in the set   The reasoning is as follows  say you have 4 items   A B C D   The number of items that can be paired with A is 3  or n-1   AB AC AD   It follows that the number of items that can be paired with B is n-2  because B has already been paired with A    BC BD   and so on      n-1     n-2           n- n-1     which is the same as  1   2          n-1    or  n n-1  2

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I was solving this algorithm and get stuck with the pairs part   This explanation help me a lot  https   betterexplained com articles techniques-for-adding-the-numbers-1-to-100   So to calculate the sum of series of numbers   n n 1  2   But you need to calculate this  1   2          n-1    So in order to get this you can use  n n 1  2 - n   that is equal to   n n-1  2

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This is how you can approach these problems in general on your own   The first of the pair can be picked in N   100  ways  You don t want to pick this item again  so the second of the pair can be picked in N-1   99  ways  In total you can pick 2 items out of N in N N-1     100 99 9900  different ways   But hold on  this way you count also different orderings  AB and BA are both counted  Since every pair is counted twice you have to divide N N-1  by two  the number of ways that you can order a list of two items   The number of subsets of two that you can make with a set of N is then N N-1  2    9900 2   4950

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What you re looking for is n choose k   Basically     For every pair of 100 items  you d have 4 950 combinations - provided order doesn t matter  AB and BA are considered a single combination  and you don t want to repeat  AA is not a valid pair

[database] How do I get the total number of unique pairs of a set in the database?

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