SOLUTION: mr. santos has set 8 questions for a math test. d.) if the most difficult question and the easiest one cannot be set next to each other, how many permutations are there for 8 qu

Question 1173253: mr. santos has set 8 questions for a math test.
d.) if the most difficult question and the easiest one cannot be set next to each other, how many permutations are there for 8 questions?
can u please show me the solution. thank you so much
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!

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

In my previous post (see the link at the end of this post), I explained that there are 8! = 40320 permutations for 8 items. I also explained that there are 2*7! = 2 * 5040 = 10080 permutations, where the most difficult and easiest questions go next to each other (= are neighbors). Hence, the number of those permutations, where these questions ARE NOT neighbors is the difference 40320 - 10080 = 30240. ANSWER

Solved.

It is the link to the referred post

https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1173252.html

https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1173252.html

==============

If you want to see many similar solved problems on PERMUTATIONS, see my lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Special type permutations problems
    - Problems on Permutations with restrictions
    - 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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