Math Is Fun Forum

Gareth

Guest

Formula for permutation of three letters in n sets

Hi

I want a formula that can calculate the number of possible permutations of ABC in sets of n.

For example, there are 81 combinations of ABC for a set of 4 digits:

AAAA
AAAB
AAAC
AABA
AABB
AABC
AACA
AACB
AACC
ABAA
ABAB
ABAC
ABBA
ABBB
ABBC
ABCA
ABCB
ABCC
ACAA
ACAB
ACAC
ACBA
ACBB
ACBC
ACCA
ACCB
ACCC
BAAA
BAAB
BAAC
BABA
BABB
BABC
BACA
BACB
BACC
BBAA
BBAB
BBAC
BBBA
BBBB
BBBC
BBCA
BBCB
BBCC
BCAA
BCAB
BCAC
BCBA
BCBB
BCBC
BCCA
BCCB
BCCC
CAAA
CAAB
CAAC
CABA
CABB
CABC
CACA
CACB
CACC
CBAA
CBAB
CBAC
CBBA
CBBB
CBBC
CBCA
CBCB
CBCC
CCAA
CCAB
CCAC
CCBA
CCBB
CCBC
CCCA
CCCB
CCCC

I want to work out how many combinations for a set of 7 digits (or indeed, any set).

Many thanks,
Gareth

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formula for permutation of three letters in n sets

Hi Gareth;

Your example does not show any restrictions so for 7 digits in 4 boxes you get 7^4 = 2401.

For n digits in b boxes you get n^b.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Formula for permutation of three letters in n sets

hi bobbym and Gareth,

I assumed that letters A, B and C were to be used rather than numbers.

If n = 1 then there are three possibilities.

If n = 2 then there are three for the first together with three for each of those, for the second = 3 x 3 = 9

If n = 3 then all of those 9 times by another three for the third letter = 9 x 3 = 27

If n = 4 then all of those 27 times by another three for the fourth letter = 27 x 3 = 81 (as you have found)

So you can continue in this way

n = 7, there are 3^7 = 3 x 3 x 3 x 3 x 3 x 3 x 3 ways

In general 3^n

If there are m distinct choices for each space then   m^n

Hi bobbym,

We seem to have arrived at the same formula. 

Bob

Last edited by Bob (2014-02-13 22:43:29)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formula for permutation of three letters in n sets

Hi Bob;

Based on his one example, that is correct!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Formula for permutation of three letters in n sets

hi bobbym,

What do you make of  this?

http://www.mathisfunforum.com/viewtopic.php?id=20503

Seems to me there's something missing (could be my brain cells) as I cannot eliminate 't' from the statements.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Formula for permutation of three letters in n sets

Hi Bob;

Sorry, I can not offer any advice. I am the last programmer ( and the first one too ) to get by with just a minimal ( I know what T and F stand for ) amount of Logic.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Formula for permutation of three letters in n sets

Oh.

Some logic statements are always true so you can substitute new statements into the variables.

But this appears to be fixed value statements, so you can only manipulate then using logic style algebra.  As he wants to end up with a statement containing only p, q all the rest have to go.  But 't' only occurs once.  It's like trying to solve simultaneous equations when you cannot eliminate a variable.

I also don't think his step 5 is right.

Oh well.  Maybe someone will jump in.  I'll go and get on with stuff in my new workshop.    At least wood doesn't argue back.

Bob

bye for now

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob