Print all possible combination of words of length 10 from a list letters with repeating 'A' exactly twice

Question

I have a list of 5 letters ['A', 'B', 'N', 'M','E'].

I want to print all the words (word means a sequence of letters, it doesn't have to be a valid English word) of length 10 letters that have exactly two letters A. Order is important.

I have tried with itertools.product as it appeared to be the most promising solution:

from itertools import product

letters = ['A', 'B', 'N', 'M','E']

for word in product(letters, repeat=10):
    res = ''.join(str(x) for x in word)
    print(res)

The problem with this approach is that I can't really control the number of occurrences of the letter A as it returns the word composed of 10 letters of A.

Is there a solution for this? Thanks

EDIT 1 Example of possible words: BANAMEMNEB : it has only twice the letter A, we don't care about other letters.

Answer 1

The way to do it efficiently is to iterate over all combinations of the positions of the letters 'A', and for each such combination - iterate over all the ways other letters can be positioned, and just insert the 'A's there.

Be warned that with your inputs this will produce almost 3 million words!

On my machine it was printing the words for so long that I had to manually stop execution.

So here is the smaller example:

letters = ['A', 'b', 'c']
num_As = 2
num_total = 4

from itertools import combinations, product
for indices_A in combinations(range(num_total), num_As):
    for rest in product(letters[1:], repeat=num_total - num_As):
        rest = list(rest)
        for index_A in indices_A:
            rest.insert(index_A, 'A')
        print(''.join(rest))

AAbb
AAbc
AAcb
AAcc
AbAb
AbAc
AcAb
AcAc
AbbA
AbcA
AcbA
AccA
bAAb
bAAc
cAAb
cAAc
bAbA
bAcA
cAbA
cAcA
bbAA
bcAA
cbAA
ccAA