Permutations

StarPhoenix · Post by **StarPhoenix** » 15 Mar 2010, 10:04

I have a bee in my bonnet

In order to distract myself from thinking about a puzzle that my boss sent me, I started thinking about
the number of ways in which the letters of the alephbeth can be combined....

How would one go about calculating the number of ways one thing can be combined with another.

I get that 1 item can be combined with 3 items in 3 ways and that 2 items can be combined with 3 items in 6, while 3x3

gives nine combinations, but am nit sure whether this is enough information from which to generalise a formula if one

to calculate the number of ways in which one can combine par of letters of the alphabet for example

a – a

a – b

a – c

….

A – Z

26 combinations for A it seems

Now I would guess that b would combine with itself and 25 other letters

C with self and 25

D with self and 25

E with self and 25

….

Z with self and 25

I am treating ab and ba as separate

Would this work out to 26x26 combinations or am I missing something?

Please point me in the right direction before this drives me nuts.

Mykhal · Post by **Mykhal** » 15 Mar 2010, 10:07

From what I remember from my Statistical Theory (about 20 years ago!) is that n! features somewhere. n! : eg 3! = 1x2x3 = 6, 4! = 1x2x3x4 = 24 etc!
So the number of possible combinations increase exponentially!

StarPhoenix · Post by **StarPhoenix** » 15 Mar 2010, 10:18

What is "!" when it is not an exclamation mark?

So it would be 26x25x24x.....x1 ?

Post by **Monty** » 15 Mar 2010, 10:21

StarPhoenix wrote:I am treating ab and ba as separate

So what you want is permutations, not combinations.

If you want to permute the entire alphabet (26 characters) without repeating characters, you would use 26! (factorial) which would be 26x25x24x23x22x21x20x19x18x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1

If you want to permute with repeats of characters, it would be 26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26x26
(or 2626)

Would this work out to 26x26 combinations or am I missing something?

26 x 26 would only be for 2 characters - with repeats

Post by **Anakha56** » 15 Mar 2010, 10:23

/exits thread with smoke coming out of my ears...

Tribble · Post by **Tribble** » 15 Mar 2010, 10:36

/Follow Anky.

They did something like this to work out the possible combination for the lotto. I understood it both times - but cannot explain it.

Post by **Monty** » 15 Mar 2010, 10:44

The possible combinations for the lotto are (47x46x45x44x43x42)/2 or 3 865 526 280

Website · Post by **hamin_aus** » 15 Mar 2010, 11:30

Derp.

Prime · Post by **Prime** » 15 Mar 2010, 13:24

Expanding on what monty said about the lotto. For the lotto one, you initially have 47 numbers to take from. Then you have 46 and then 45.

So that's 47 ways to pick the first number, 46 to pick the second, 45 to pick the third.

StarPhoenix · Post by **StarPhoenix** » 15 Mar 2010, 13:47

We are duly impressed.

I think I get this.

I was looking for alphabet permutations with repeats, ie 26^26.

Well now I know who to ask when next I am puzzling over something of this nature.

What is the difference between a permutation and a combination, by the way?

Post by **Monty** » 15 Mar 2010, 13:58

http://www.mathagonyaunt.co.uk/STATISTI ... combs.html

in a permutation, order matters - so 1234 is different to 1243
where as in a combination, order doesn't matter so 1234 and 1243 considered the same as they have the same digits.

VoxynQueen · Post by **VoxynQueen** » 17 Mar 2010, 02:38

I would have just used my calculator.
It has a permutation and combination button on it.

Otherwise use the formula that Monty gave.

Prime · Post by **Prime** » 17 Mar 2010, 07:32

You'd be surprised how many students in my stats class sit and type out the formula for C and P

VoxynQueen · Post by **VoxynQueen** » 17 Mar 2010, 14:25

I teach some kids maths too.
Even the brightest ones are too stupid to play on their calculators to see how they work.
For example, typing out *10^ instead of pressing the EXP button.
Not know how to store things in memory.

For some bizarre reason they are also all afraid of fractions and try to make everything into a decimal.

Prime · Post by **Prime** » 17 Mar 2010, 14:38

VoxynQueen wrote:I teach some kids maths too.
Even the brightest ones are too stupid to play on their calculators to see how they work.
For example, typing out *10^ instead of pressing the EXP button.
Not know how to store things in memory.

For some bizarre reason they are also all afraid of fractions and try to make everything into a decimal.

And they are not taught to use them properly at school level. you can do coordinate systems, degrees minutes, seconds, regression, etc.

Moses · Post by **Moses** » 17 Mar 2010, 16:08

Monty wrote:The possible combinations for the lotto are (47x46x45x44x43x42)/2 or 3 865 526 280

Why are you dividing by 2? And are there not 49 numbers in our lotto?

Post by **Monty** » 17 Mar 2010, 16:34

Moses wrote:
Monty wrote:The possible combinations for the lotto are (47x46x45x44x43x42)/2 or 3 865 526 280
Why are you dividing by 2? And are there not 49 numbers in our lotto?

Oops. Yes, there are 49 lotto numbers (Guess who has never played lotto before)

And it should be (49x48x47x46x45x44)/(6x5x4x3x2x1) or 13 983 816

endev8003 · Post by **endev8003** » 17 Mar 2010, 16:45

That looks still wrong.

It should be just (49x48x47x46x45x44) which is 10 068 347 520.

Moses · Post by **Moses** » 17 Mar 2010, 16:47

endev8003 wrote:That looks still wrong.

It should be just (49x48x47x46x45x44) which is 10 068 347 520.

Wrong. Monty is now correct.

Post by **Monty** » 17 Mar 2010, 16:54

endev8003 wrote:That looks still wrong.

It should be just (49x48x47x46x45x44) which is 10 068 347 520.

No. That is permuations - ie order of the numbers matter.
The lotto just uses the numbers (order doesn't matter) so you need a combination not permutations.

Mykhal · Post by **Mykhal** » 19 Mar 2010, 10:38

Monty wrote:
endev8003 wrote:That looks still wrong.

It should be just (49x48x47x46x45x44) which is 10 068 347 520.
No. That is permuations - ie order of the numbers matter.
The lotto just uses the numbers (order doesn't matter) so you need a combination not permutations.

Just a stupid question - shouldn't it be (49x48x47x46x45x44x43.....x2)?

SykomantiS · Post by **SykomantiS** » 19 Mar 2010, 11:03

No, then you'd be using all 49 numbers for the combo, not just 6 of the 49 (I think- my maths is waaay rusty

)

Post by **Monty** » 19 Mar 2010, 11:04

Mykhal wrote:
Monty wrote:
endev8003 wrote:That looks still wrong.

It should be just (49x48x47x46x45x44) which is 10 068 347 520.
No. That is permuations - ie order of the numbers matter.
The lotto just uses the numbers (order doesn't matter) so you need a combination not permutations.
Just a stupid question - shouldn't it be (49x48x47x46x45x44x43.....x2)?

No. You are only using six numbers for the lotto.

So for the first number you have 49 choices
So for the second number you have 48 choices
So for the third number you have 47 choices
So for the forth number you have 46 choices
So for the fifth number you have 45 choices
So for the sixth number you have 44 choices
So 49 x 48 x 47 x 46 x 45 x 44

And as the order doesnt matter, you need to divide by 6 x 5 x 4 x 3 x 2 x 1

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