# Thread: Prob of a letter bag from a set of letters

1. ## Prob of a letter bag from a set of letters

Say I have a set of letters totaling n (say 80 for ex)
(some letters may occur more than once in this set)

I randomly choose r letters from n (say r= 4)
What is the probability of seeing the letter bag
'aabcd' (it's a bag so order doesn't matter, 'adcab' is also ok)
Note that there are 2 a's in this bag.

The general form of the bag is:
k_a of letter a
k_b of letter b
..
all total to k

Assuming that there are n_a of letters a
n_b of letters b
n_c of letters c
and so on .. all total to n
from the set of n letters

[n_aCk_a * n_bCk_b * ... ] / nCr

And I know this is not correct
Can anybody help me get the correct answer for this?

Thanks

2. ## Re: Prob of a letter bag from a set of letters

Hey lettertha.