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

52

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?

This question is tagged with database math

~ Asked on 2013-09-17 20:36:21

The Best Answer is


79

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

~ Answered on 2016-06-15 23:33:35


72

What you're looking for is n choose k. Basically:

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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).

~ Answered on 2013-09-17 20:39:49


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