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 ..

from the set of n letters

My naive answer is

[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