SOLUTION: 1: A figure skating coach has 20 athletes and wishes to select 8 to take to a training trip. How many different ways could he select these 8 athletes? 2: The figure skating co

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Question 1195868: 1: A figure skating coach has 20 athletes and wishes to select 8 to take to a training trip. How many different ways could he select these 8 athletes?

2: The figure skating coach decides to enter 6 athletes into a competition. If no ties are allowed, how many different top-two orders are possible for these 6 athletes?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

(1)  There are   =  = 125970 different ways to select 8 athletes from 20 athletes.    ANSWER


It is the number of combinations of 20 persons taken 8 at a time.


Notice that the order of selection does not matter in this problem - therefore, we use COMBINATIONS.

Solved, answered and explained.

----------------

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.



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