Maths

[V8mate]

Something which has been gnawing away at me (for a solution).

If you take the letters ABCDEF - the number of different ways you can write those six characters is a simple exponential; i.e. 6! = 6x5x4x3x2x1 = 720

However, if each of those characters could be 'any letter of the alphabet', rather than the fixed character moving about in the line-up, how do you work out (I don't just want the final answer) the number of letter combinations?

[Alex]

26^26

Edited to add: which equals 6.1561195802071573107966742884002e+36

Edited by Alex on Saturday 23 May 09:36

[V8mate]

Alex said:

26^26

How does that factor in that you are only selecting 6 characters at any one time though? (Perhaps I didn't make that clear in my OP )

[esselte]

Is this any nearer..


26!/(6!*(26-6)!)

[V8mate]

esselte said:

Is this any nearer..


26!/(6!*(26-6)!)

Is that just a pile of made-up stuff? Or can you explain the rationale?

[esselte]

It's just probability

number of combinations = n!/((n-r)!r!)
where:
n = number of items to choose from
r = number of items chosen

It's the same formula that gives you a 1 in 13.5 million chance of winning the national lottery.I'm assumng you can't pick the same letter twice?

[Alex]

V8mate said:

Alex said:

26^26

How does that factor in that you are only selecting 6 characters at any one time though? (Perhaps I didn't make that clear in my OP )

You said 'any letter of the alphabet'.

If you can select any letter of the alphabet in 6 positions, then the answer is 26^6 = 308915776.

[esselte]

Alex said:

V8mate said:

Alex said:

26^26

How does that factor in that you are only selecting 6 characters at any one time though? (Perhaps I didn't make that clear in my OP )

You said 'any letter of the alphabet'.

If you can select any letter of the alphabet in 6 positions, then the answer is 26^6 = 308915776.

We're answering 2 different questions here aren't we? You're assuming we can repeat letters,I'm assuming we can't.....

[Alfanatic]

C'mon guys! It's a Saturday! And it's sunny!!!

[V8mate]

esselte said:

Alex said:

V8mate said:

Alex said:

26^26

How does that factor in that you are only selecting 6 characters at any one time though? (Perhaps I didn't make that clear in my OP )

You said 'any letter of the alphabet'.

If you can select any letter of the alphabet in 6 positions, then the answer is 26^6 = 308915776.

We're answering 2 different questions here aren't we? You're assuming we can repeat letters,I'm assuming we can't.....

I think you should assume you can repeat letters.

[esselte]

V8mate said:

esselte said:

Alex said:

V8mate said:

Alex said:

26^26

How does that factor in that you are only selecting 6 characters at any one time though? (Perhaps I didn't make that clear in my OP )

You said 'any letter of the alphabet'.

If you can select any letter of the alphabet in 6 positions, then the answer is 26^6 = 308915776.

We're answering 2 different questions here aren't we? You're assuming we can repeat letters,I'm assuming we can't.....

I think you should assume you can repeat letters.

In that case Alex is correct...it's like saying how many ways can you arrange 3 numbers from 0-10,you can have any sequence from 000 to 999 ie 1000 combinations which is 10^3 ..... HTH

[V8mate]

Thanks guys