SOLUTION: On this page: https://www.algebra.com/algebra/homework/Permutations/change-this-name6021.lesson Why has this been wrong for ten years? The correct answer is 606. < exce

Algebra.Com
Question 1136585: On this page:
https://www.algebra.com/algebra/homework/Permutations/change-this-name6021.lesson
Why has this been wrong for ten years? The correct answer is 606.
< excerpt from page follows ...
EXAMPLE:
Q. How many different 4 letter "words" can you make from the word DAFFODIL?
A: The number of permutations is P(8,4) since permutations do not distinguish between DAFF and DAFF, for example: If I had written DAFfOdIL instead, you can now see the differences as DAFf and DAfF.
The question is one of permutations and not combinations, since in this example, we are definitely interested in DAFF, ADFF, FFAD, FADF etc being different "words" rather than duplicate versions of the same "combination" of 4 letters.
So, the total number of permutations is 1680. However, 1680 is not the correct answer, since we have 2 D's and 2 F's.
The correct answer is 1680/(2.2) --> 420.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

1.  This lesson was written not by me, so I am not responsible for its contents . . . 



2.  My opinion is that @longjonsilver, the author of that lesson, is a very good tutor.

    This opinion is based on reading his numerous lessons in the site www.algebra.com and his posts to the forum.

    Unfortunately, just for a long time I do not see new contributions from him at this site and the forum.



3.  That fragment from his lesson you refer to - is not his best (or even regular) writing - it is really UNREADABLE and nonUNDERSTANDABLE.



4.  This fragment is about permutations of letter in a word, which contain identical letters.


    All you need to know on this subject, you can read from MY lesson

        Arranging elements of sets containing indistinguishable elements 

    in this site.



5.  So, ignore that passage and learn the subject from my lesson, instead.

    May be, the best service that I can do in this case is to take off (to cut off) this fragment from his lesson . . . 


    Thank you for noticing it !



6.  If you have more questions - do not hesitate to ask them.

    We, the tutors at this forum, will be happy to answer.

Happy learning !


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

On Combinations and Permutations,  see the lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Problems on Permutations
    - Math circle level problem on Permutations
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Math circle level problem on Combinations
    - Arranging elements of sets containing indistinguishable elements
    - Persons sitting around a cicular table
    - Combinatoric problems for entities other than permutations and combinations
    - Miscellaneous problems on permutations, combinations and other combinatoric entities
    - In how many ways N distinguishable objects can be distributed among n different boxes ?
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

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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