SOLUTION: Determine the number of combinations of 20 things, taken four(4) at a time

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Question 1193865: Determine the number of combinations of 20 things, taken four(4) at a time
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

Use the standard formula for the number of combinations

    C%5B20%5D%5E4 = 20%21%2F%284%21%2A%2820-4%29%21%29 = 20%21%2F%284%21%2A16%21%29.


Reduce common factors 16! in the numerator and the denominator.  The formula takes the form

    C%5B20%5D%5E4 = %2820%2A19%2A18%2A17%29%2F%281%2A2%2A3%2A4%29 = use your calculator = 4845.      ANSWER

Solved.

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This problem is on COMBINATIONS.


On  Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

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.



Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Start with 20, go down 1 at a time multiplying until you have 4 factors
on top.

Then there are also 4 factors on the bottom, starting with 4, going down 1
at a time until you have 4 factors on the bottom. 


like this:


%2820%2A19%2A18%2A17%29%2F%284%2A3%2A2%2A1%29

Then figure that out.

Edwin