Question 1144395: A local Yacht Club holds a sailing regatta once a week. The start of the race is determined by the direction of the wind (East/West/North/South). There is a total of nine (9) buoys (Letter A- to Letter I ), but only four (4) buoys are selected each week for the race course. How many race course permutations can be derived given the wind direction? What are these combinations?
Answer by ikleyn(52910)   (Show Source):
You can put this solution on YOUR website! .
I think that not all the tutors at this forum are yachtsman (or yachtswoman), and the true meaning of this post
(of this problem) is not exactly clear to me : toooo many unnecessary words are placed in it
(standard American style formulating Math problems, UNFORTUNATELY), instead of placing right words in a right order.
But if you want to ask, in how many ways 4 different buoys can be selected among 9 distinguishable buous,
then the answer is
 =  =  = 126.
It is the number of COMBINATIONS of 9 items taken 4 at a time.
It assumes that the order of these 4 buoys does nor matter.
If, in opposite, the order of 4 selected buoys DOES MATTER, then we should consider PERMUTATIONS, and
the answer to the problem's question is
9*8*7*6 = 3024 ways.
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For introductory lessons on PERMUTATIONS and COMBINATIONS see the lessons
- Introduction to Permutations
- PROOF of the formula on the number of Permutations
- Problems on Permutations
- Introduction to Combinations
- PROOF of the formula on the number of Combinations
- Problems on Combinations
- OVERVIEW of lessons on Permutations and 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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My personal opinion is that until american educational system / textbooks will use such style of formulating problems
in Math as we see in this post -- it will be dead and will remain to be dead, as it is and as we see it now (last 20 - 30 years).
Although it still is able to teach students to make routine operations and solve routine problems,
it is not able to inspire students and to teach them to think.
I saw thousands such problems, where their authors major goal is to demonstrate and to prove their art in using English,
but all these formulations are/were terrible from the common sense view.
I also observed many times this sad correlation that than better is English in formulating such problems, than worst is
their mathematical meaning and educational value.
Surely, it does not relate to professional writers of Math textbooks for schools,
but relates in great extent to so called amateurs who try to create Math problems on their own.
Until the system will feed students with the problems, formulated in this way, they will hate Math.
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