Maths

[Onlyforfun]

Can't remember the formula for claculating the number of combinations from a number of selections, e.g., combinations of 3 from 6 selections.

Is it:

x= no. of selections
y= no. of selections in combination

(x!/y!)/(x-y)!

[markwales]

Right here ya go..........

x! / (x-y)!*y!

So

6! / (6-3)!*3! = 6! / (3!*3!) = 720/(6*6) = 720/36 = 20.........EASY !!...lol

[Workshy]

Combinations
When we want to find the number of combinations of size 2 without repeated letters that can be made from the three letters in the word CAT, order doesn't matter; AT is the same as TA. We can write out the three combinations of size two that can be taken from this set of size three:

CA CT AT
We say '3 choose 2' and write 3_C_2. But now let's imagine that we have 10 letters from which we wish to choose 4. To calculate 10_C_4, which is 210, we don't want to have to write all the combinations out!

Since we already know that 10_P_4 = 5040, we can use this information to find 10_C_4. Let's think about how we got that answer of 5040. We found all the possible combinations of 4 that can be taken from 10 (10_C_4). Then we found all the ways that four letters in those groups of size 4 can be arranged: 4 x 3 x 2 x 1 = 4! = 24. Thus the total number of permutations of size 4 taken from a set of size 10 is equal to 4! times the total number of combinations of size 4 taken from a set of size 10: 10_P_4 = 4! x 10_C_4.

When we divide both sides of this equation by 4! we see that the total number of combinations of size 4 taken from a set of size 10 is equal to the number of permutations of size 4 taken from a set of size 10 divided by 4!. This makes it possible to write a formula for finding 10_C_4:

10_P_4 10! 10!
10_C_4 = -------- = ------- = ----------
4! 4! x 6! 4!(10-4)!


10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= --------------------------------------
4 x 3 x 2 x 1 (6 x 5 x 4 x 3 x 2 x 1)


10 x 9 x 8 x 7 5040
= -------------- = ------ = 210
4 x 3 x 2 x 1 24


More generally, the formula for finding the number of combinations of k objects you can choose from a set of n objects is:

n!
n_C_k = ----------
k!(n - k)!

For our CAT example, we do the following:

3! 3 x 2 x 1 6
3_C_2 = ------ = ----------- = --- = 3
2!(1!) 2 x 1 (1) 2

[Workshy]

Oops :doh

[MarcusMel]

Nice try Workshy but you have fallen fowl of the famous W2W formating.

That is it seems to ignor tab's and spaces.

[Workshy]

Arrrh well, Markyboy done the biz :) Mine was a copy & paste as I didnt pay much attention in Maths A-Level!

[sparkyminer]

I did learn all the above malarkey, then the last calculator I bought had this button on:- nCr, does it all for you.

[vegyjones]

6! / (3!*3!) = 720/(6*6)

How does that happen then???
That's

6 / 9

isn't it??

What are we trying to work out anyway,
how many combinations of 3 between 6 horses... is that right???

I'm purplexed! :D

[sparkyminer]

The secrets in the exclamation mark Vegy.

[markwales]

! = Factorial

So 6! = 6*5*4*3*2*1 = 720

[plater]

Combinations easy peasy in plain speak :D

Any 3 from 6 = 6*5*4 / 1*2*3

Any 2 from 6 = 6*5 / 1*2

Any 4 from 10 = 10*9*8*7 / 1*2*3*4

Any 2 from 10 = 10*9 / 1*2

Any 6 from 10 = 10*9*8*7*6*5 / 1*2*3*4*5*6

The 8 from 10 on the pools is 45 lines = 10*9*8*7*6*5*4*3 / 1*2*3*4*5*6*7*8

[Jonny2621]

Has this forum changed from the English language ? Ooo

[sparkyminer]

And 6 from 49 is 13983816.
Does that ring a bell with anyone.

[Workshy]

Yeah, lottery theives!

[sparkyminer]

Yeah, lottery theives!
Pay that man. :)

[Onlyforfun]

What have I started!!! :yikes:


(thanks btw)

[MattR]

The answer is 42. According to the hitchhikers guide to the galaxy anyway.

[Onlyforfun]

:D

My favourite series of books ever.

[bigcumba]

Very funny! I have the BBC radio series as well - brilliant stuff - as were the Dirk Gently books :)

[mathare]

Be interesting to see how the film version they are making turns out

[bigcumba]

Yeah, that will be worth seeing - as long as they don't do the hollywood thing and change it too much as with that crap She-Devil film...

[MarcusMel]

;fire BBC radio series is a cut down version of the origional broadcast.

Copywright problems I think.

[bigcumba]

Ahh, must check that out Marcus - bought it around 7 or 8 years ago I think as a box set... another one I have is the Lord Of The Rings BBC radio drama series - it's brilliantly done, with Michael Hordern as Gandalf - talk about inspired casting! Well worth checking out if you're a LOTR fan!

[podtog]

Stick to level stakes, much easier. :)

[MarcusMel]

The bit I soarly miss is when they land on Magrathea (mind the whale meat) and Marvin hums like 'Pink Floyd' ;fire THEY CUT IT OUT Arrrgh.

Then I noticed that I felt as if other little bit here and there were missing too but comparason was not easy.

[radders]

Ahh, must check that out Marcus - bought it around 7 or 8 years ago I think as a box set... another one I have is the Lord Of The Rings BBC radio drama series - it's brilliantly done, with Michael Hordern as Gandalf - talk about inspired casting! Well worth checking out if you're a LOTR fan!

Hi Big C,

Did you ever catch the R4 series "Hordes of the Things"?

Probably late '70's early '80's.

A fantastic send up og LOTR & all things Moorcock & Sword & Socery related.

There there are all sorts of D & D type gaming sites derived from this, but the radio series is well worth trying to track down for such gems as "skulking behind these bushes is no Princley task...."

Regards
Radders

[bigcumba]

No, haven't heard of that - I'll try and see if I can get hold of it via Shareazaa - I like spoofs of classics like that as long as they're done well. I've read the old 'Bored Of The Rings' book done by the National Lampoom folk back at the end of the 60's. It's about 1200 pages shorter as well! Like a lot of the Moorcock stuff as well - obviously being a Hawkwind fan I had to check out the Elric books - brilliant stuff!

[MarcusMel]

One of my favorites, if I may interupt along a diverse line, is

"I learned everything I need to know about life by watching Star Trek"

:doh I think that is the title.

[bigcumba]

My wife is becoming a bit of a Star Trek fan these days, so I'm not complaining! I think it stems from watching another spoof - Galaxy Quest - about 40 times in the last couple of years! Very funny movie if you're a fan of the various Trek series!

[tipp]

Without algabra. The lotto odds,
49 times 48 = 2352 divided by 2 = 1176 Doubles
1176 times 47 = 55272 divided by 3 = 18424 Trebles
18424 times 46 = 847504 divide by 4 = 211876 fourfolds
211876 times 45 = 9534420 divide by 5 = 1906884 fivefolds
190688 times 44 = 83902896 divide by 6 = 13983816 sixfolds

BINGO

Therefore
6 times 5 = 30 divided by 2 = 15 Doubles
15 times 4 = 60 divided by 3 = 20 Trebles XXXX
20 times 3 = 60 divided by 4 = 15 fourfolds
15 times 2 = 30 divided by 5 = 6 fivefolds
6 = 1 sixfold

Be Lucky
Tipp

[Win2Win]

Next person to mention the Lotto on here will have his goolies strubg up next to a behive and covered in pollen :yikes: :)

[tipp]

Is that good for your ging gang's.