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?