SOLUTION: five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if a. Couples must stay together? b. They may stand anywhere?

Question 1178588: five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if
a. Couples must stay together?
b. They may stand anywhere?
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.


(a)  Considering five couples as five special objects,

     we have 5! = 5*4*3*2*1 = 120 permutations of these objects.



     Next, we have 2 possible permutations (A,B) --> (B,A)  inside each of 5 pairs.

    
     These permutations are independent ---  so, there are   = 32*120 = 3840 permutations of 5 couples, satisfying the imposed conditions.




(b)  If no restrictions are imposed, then there are 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 possible permutations of 10 persons.

Solved.

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

On Permutations, see introductory 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.

RELATED QUESTIONS
please help me! Four married couples have reserved eight seats in a row at the... (answered by stanbon)

Four married couples have reserved 8 seats in a row at the theatre, starting at an aisle... (answered by longjonsilver)

How many ways can 3 couples sit in a row in a movie theater if all couples must sit... (answered by robertb)

In how many ways can 4 married couples seat themselves around a circular table if they... (answered by ikleyn)

How many ways can four couples be seated in a row of eight seats? (a)if couples are... (answered by ewatrrr)

4 married couples have 8 seats in arrow at the theater, starting at an aisle seat. In how (answered by kevwill)

In how many ways can five couples be seated in a row of 10 chairs if no couple is... (answered by stanbon)

in how many ways can five couples be seated in a row if a. there are no restrictions?... (answered by ikleyn)

Four married couples have bought eight seats in a row for a basketball game. In how many... (answered by fractalier)