need equation for determining how many combinations of 9 non repeating letters out of a pool of 26 letters.?

Question

I need to know how many combinations of 9 non-repeating letters I can make out of a pool of 26 letters. I would like to know the equation to so I can change the number of non-repeating letters.

Answer 1

If you select 9 unique letters from a pool of 26, you use the combination function, in which x is the number of objects, and y is the number you're selecting. This can be read as "x choose y".

Com[x, y]
= x! / (y! * (x-y)!)

So:

Com[26, 9]
= 26! / (9! * (26 - 9)!)
= 26! / (9! * (17)!)
= 3124550

Answer 2

This is just nCr = n!/( r! (n-r)! )
where n = size of pool = 26
and r = #letters chosen = 9

For n=26, r=9 this simplifies to
(26)(25)(24)(23)(22)(21)(20)(19)(18) divided by (1)(2)(3)(4)(5)(6)(7)(8)(9)

Answer 3

The first part of your question--how many combinations.
26!/[9!(26-9)!]=3260400 (better check, no calculator handy).

The formula looks like this n!/[k!(n-k)!], where n is the pool, and k is the number of elements pulled from the pool. Check out wikipedia for more info.

Answer 4

26C9 = 26!/[(26-9)!9!] = 26!/[17!9!] =

(26*25*24*23*22*21*20*19*18) / (9*8*7*6*5*4*3*2*1)

nCr = n!/[(n-r)!r!]

Answer 5

by non repeating- do you mean there are none of the same letters- or just each letter cant have the same letter before or after it

for the first

26x25x24x23x22x21x20x19x18

for the latter

26x25x25x25x25x25x25x25x25

Answer 6

nCr= n!/ r!(n-r)! = nPr/r! = (26x25x24x23x22x21x20x19x18)/ (9x8x7x6x5x4x3x2x1) =10015005