SOLUTION: Taking an algorithm course and working a union-find problem. Algebra & trig too long ago (high school in 1970s) to remember how to calculate permutations. If I have N objects how

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Question 1172654: Taking an algorithm course and working a union-find problem. Algebra & trig too long ago (high school in 1970s) to remember how to calculate permutations. If I have N objects how many union operations do I need for each object to paired with every other object in the set? I looked at permutation and combination formulas and do not understand the ! symbol.
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

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 %28N%2A%28N-1%29%2F2%29    (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.