Question 1150497: Find the number of ways 5 people can sit in a row where: (a) there are no restrictions; (b) two of the people insist on
sitting next to each other.
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
(a) 5! = 5*4*3*2*1, the number of permutations of 5 objects.
(b) 2*4! = 2*4*3*2*1 we consider the particular pair as one object,
and then we permut 5-1 = 4 objects, which gives 4! into the formula.
Then we recall that this pair, in each and every its position in the row, can be in any of
the two states, (A,B) or (B,A), which gives us an additional factor of 2.
Solved, answered and explained.
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On Permutations, see introductory lessons
- Introduction to Permutations
- PROOF of the formula on the number of Permutations
- Problems on Permutations
- 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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