.
From your post, I do not understand clearly the exact meaning of the problem.
So, I only can/may guess.
If you need to find the number of pairs, which you can create using n objects,
then the answers are as follow:
a) if we combine different objects in pairs and if the order is important,
then the number of pairs is N*(N-1) (permutations).
b) if we combine different objects in pairs and if the order is NOT important,
then the number of pairs is (combinations).
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For introductory lessons on permutations and combinations, see
- Introduction to Permutations
- PROOF of the formula on the number of Permutations
- Simple and simplest problems on permutations
- Introduction to Combinations
- PROOF of the formula on the number of Combinations
- Problems on Combinations
- Miscellaneous problems on permutations, combinations and other combinatoric entities
- Fundamental counting principle problems
- Nice recreational problems on permutations
- OVERVIEW of lessons on Permutations and Combinations
in this site. // I listed here the "introductory" lessons only . . .
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.