Question 1180839: Molly, Mary, Michael, and Melissa are all standing together.
(a) In how many ways can they be arranged in a circle? Is it (5-1)!??
(b) In how many ways can they be arranged in a circle if Molly and Melissa must stand together? Is it 2! x 3! ??
(c) In how many ways can they be arranged in a circle if Molly and Melissa can't stand together?
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
(a) In (4-1)! = 3! = 1*2*3 = 6 different ways.
In this problem, special type of permutations is considered: CIRCULAR permutations - - - NOT LINEAR permutations.
Number " 5 " in your post is IRRELEVANT.
---------------------
To see many other similar (and different) solved problems on CIRCULAR PERMUTATIONS, look into the lesson
- Persons sitting around a cicular table
in this site, and learn the subject from there.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is 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.
////////////////
AVOID posting many problems/questions in one post.
POST THEM SEPARATELY, especially if you need detailed explanations/solutions.
One and ONLY ONE problem/question per post.
It is the RULE, the POLICY and the REQUIREMENT of this forum.
It is written in this page
https://www.algebra.com/tutors/students/ask.mpl?action=ask_question&topic=Equations&return_url=http://www.algebra.com/algebra/homework/equations/
from which you post your problems.
It is assumed that you read these rules before posting.
It is also assumed that you do understand what is written in that page and follow the rules.
Those who violate them, work against their own interests.
*******************************************************************
So P L E A S E post your problems S E P A R A T E L Y (!)
*******************************************************************
|
|
|
