Melody

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Melody  Feb 11, 2022
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Hi Nauseated,

 

Your answer:

Consider this the same as unique combinations of 2 from integer set {n}

1 person, 0 pair

2 persons, 1 Pair
3 persons, 3 Pairs
4 persons, 6 Pairs
5 persons, 10 Pairs
6 persons, 15 Pairs

7 persons, 21 Pairs

8 persons, 28 Pairs

nC2 unique pairs   

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

 

 

You have found how many individual pairs can be made from 8 people.

That is NOT the question.

 

If there is three people, or any odd number of people in a room, they cannot all be paired of so the question would make no sense.  There would be no answer.

 

 You have said that if there are 4 people in a room there would be 6 pairs. This is not correct.

These are the the possible combinations

AB    and   CD

AC   and   BD

AD   and   BC

There are no other possible combinations.  So there are 3 combinations.

 

If there are 6 people in a room then you are correct, there are 15 combination.

because

IF E and F are together there are 3 ways the others can be combined, as shown above.

IF E and A are together there are 3 ways the others can be combined, as shown above.

IF E and B are together there are 3 ways the others can be combined, as shown above.

IF E and C are together there are 3 ways the others can be combined, as shown above.

IF E and D are together there are 3 ways the others can be combined, as shown above.

So there is a total of 3*5 = 15 ways that 6 people can be paired off

 

Now there  there is 8 people in a room    A, B, C, D, E, F, G, H

G and H are together then there are 15 ways the others can be paired.

G and A are together then there are 15 ways the others can be paired.

G and B are together then there are 15 ways the others can be paired.

G and C are together then there are 15 ways the others can be paired.

G and D are together then there are 15 ways the others can be paired.

G and E are together then there are 15 ways the others can be paired.

G and F are together then there are 15 ways the others can be paired.

G and  are together then there are 15 ways the others can be paired.

So there are  15*7 = 105 ways that the people can be paired

etc

If there are 2n people in the room then there will be 1*3*5*7*........*(2n-1)  ways that they can be paired.

 

According to OEIS   (Online Encyclopaedia of Integer Sequences)

https://oeis.org/search?q=1%2C3%2C15%2C105%2C&language=english&go=Search

The notation for this is   (2n-1)!!

 

laugh cool laugh cheeky                                

Dec 6, 2015
 #45
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+10

@@ What is Happening?  [Wrap4]   Sat 5/12/15   Sydney, Australia Time 11:43 pm   ♪ ♫

 

Good weekend :)

Answer credits go to CPhill, Alan, Omi67, Heureka, Hayley1, Beababy, LambLamb, Geno3141, Mathcalc. buubleman and Einstein Jt.  Thanks Guys  (  That includes the girls when used by an Australian in this context   wink  ) 

 

Technical Issues

IDK, is the picture upload working - it wasn't the last time i tried it. ://

 

How can you post a picture when the picture upload on the forum is not working properly ?

Thanks very much Alan for these instructions.

http://web2.0calc.com/questions/ven-diagram-need-help-for-questions#r3

 

Interest Posts 

If you ask or answer an interesting question, you can private message the address to me (with copy and paste) and I will include it.  Of course only members are able to do this.  I quite likely will not see it if you do not show me.  

 

1)  How many trees can we plant?   Thanks CPhill and guest.  

     http://web2.0calc.com/questions/orchard-problem#r3

2)  Difficult simultaneous equations question - Thanks Chris and Alan.

     That is what martrices are used for :)

     https://web2.0calc.com/questions/simultaneous-equations-with-5-unknowns

3)  Find all solutions for sin(5x)=sin(3x)  Thanks LambLamb, CPhill, Melody and Guest.  

     https://web2.0calc.com/questions/sin-5x-sin-3x

4)  Combinations  - pairing off 8 people       Thanks Alan

     https://web2.0calc.com/questions/there-are-8-people-in-a-room-they-were-asked-to-go-in-a-certain-place-2-at-a-time-in-how-many-ways-could-the-people-be-paired-is-it-an-example-of#r2

5)  Complex number multiplication     Melody

     http://web2.0calc.com/questions/complex-numbers_48321#r1

6)   Formulating number sentences     Thanks CPhill and Melody

     These would be great practice for most students!

     http://web2.0calc.com/questions/help_35979

 

 

                                                                 ♪ ♫      Melody    ♪ ♫                                                

Lantern thread:

Dec 5, 2015