Melody

Here are some video clips that i forgot to include.     

In how many ways can 8 people be seated around a square table with 2 people on a side? (Two configurations are considered equivalent if one is a rotation of another.)

Since this question has been dredged back up I decided to pay with it again (just to check that i can still do it ).......

It reall depends on what the questioner means.

If you are treating the square table like a round table then there are (8-1)! = 5040

BUT If you rotate just one place then the pairs are different so this number is doubled

5040*2= 10080

This was Chris's original answer.

Our guest has just given you exactly the same solution, thanks for making it clear guest.  

Our guests logic was a little different from mine but it is totalyy correct (both logic and answer)

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If you only care about who is sitting in pairs and where the pairs are in relation to the otheraround the table (who is one the right or left does not matter) then the problem becomes different.

The answer would be who many pairs can be formed x how many ways can they be seated.

How many ways can the 4 pairs be seated = 3! =6

How many ways can they be fromed.

If there were only 2 people there would be 1 way.

If there were 4 people ABCD then AB, AC,AD  who A is with defines BOTH pairs so ther is 3 ways.

If people E and G join the mix  then if they are together then there are 3 ways.

Bur E could be with G or A or B or C or D   So that is 5 x3 ways.

By extention, if there are 8 people there are 7*5*3 = 105 ways they can be paired off. 

I remember someone told me the notation is 7!!

So the number of ways pairs can be chosen and the pairs seated at the table (If AB are a pair that is the same as BA)  is 105*6 = 630 ways.

If where in a pair, personApersonB is different from personBpersonA the number would be much bigger. I think then the number would be back to 10,080 again as I think it would be the same as the original problem ://

Thanks for the info Solveit, it is great having people from all corners of the world in here!

I used to teach at an International College.  I loved that too :D

I just googled your question and came up with this site.

Maybe you can find what you want here //

How would I calculate the chance of something depending on the value of it?

As our guest said, this is called probablility.

Probabilities go between zero and +1    They cannot be outside this range.

If something cannot happen then the propability of it happening is zero

If somthing has to happen then the probability of it happening is 1.

Say there are 3 green b***s and 5 red b***s in a container and you randomly choose one.

What is the chance (probability ) of choosing a red one?

3+5=8

There are 8 possible b***s you could choose.  8 is said to be the size of the "sample space."

There are 5 red b***s.  You want a red one so there are "5 favourable events"

Prob of choosing a red one = number of red ones divided by the total number of b***s.

\(P(red)=\frac{favourable \;events}{Total\; number \;in \;sample\; space}=\frac{number\; of \;red\; b***s}{Total \;number\; of \;b***s}=\frac{5}{8}\;\;or\;\;0.625\)

Yes, what our guest has said is correct.

A logarithm is an index or an exponent or a power (3 words that mean the same thing)

You can use them if you need to find a missing exponent

For example

\(If\;\;3^x=243\\ then \;\;x=log_3 243\\ x=5\;\; because\;\;3^5=243\\~\\ \)

In words

If 3 to the power of x = 243 then x = log of 243 base 3

Most calculators can only to base 10 or base e and it is easy to change from one base to another but the web2 calc can work in any positive integer base.  I will just check this ://   

log(243,3) = 4.999999999999999   near enough    4.9 repeater actually is 5 anyway://

Birthday posts:   Some anyway

https://web2.0calc.com/questions/happy-birthday-gino3141               27/12/15

(5.5*10 to the 4th power)(3*10 to the negative second pwer)

\((5.5*10^4)(3*10^{-2})\\ =5.5*3*10^4*10^{-2}\\ =16.6*10^{4+-2}\\ =16.6*10^2\\ =1660\)

What's the square root of 25 ?
Is it 5 or +/- 5 and why ?

ALSO

Say it was + or -

then there would be no way of differentiating between

9+sqrt(25)   and    10-sqrt(25)

They would both have the same 2 answers    9 + or - 5   =   14 or 4 

Mon 28/12/15

Happy birthday Gino   

http://web2.0calc.com/questions/happy-birthday-gino3141

More great stories from Dragonlance    

http://web2.0calc.com/questions/a-christmas-story-from-dragonlance-s-journal

Great geometry brain tease   

http://web2.0calc.com/questions/whoever-finds-the-solution

Finding asymptotes of a hyperbola.    (Contined)   Thanks Gino3141, Alan and Guest.

https://web2.0calc.com/questions/i-need-to-find-the-asymptotes-of-this-hyperbola-x-2-2-121-y-5-2-81-1

Completing the squares.  Great answer from CPhill

http://web2.0calc.com/questions/completing-the-square_5860

Quintic Convergence of pi (continued)  Thanks Alan and Bertie    :)

http://web2.0calc.com/questions/quintic-convergence-of-pi

Difficult Integral

http://web2.0calc.com/questions/integral-e-arctanx-1-x-2-1-2

Ordinary differential Equation

https://web2.0calc.com/questions/ordinary-differential-equation