all possible combinations of items in n lists

I need to develop a list that contains all possible combinations in order of elements in n lists. Basically, I'm trying to find all possible paths that will be needed later in another part of the program.

I've written some simple code for the two lists, but the problem is that I don't know how much input the user will give, so I have to guess. Currently, I have defined a function that outputs all possible combinations (only one way, since they are paths). I've also been testing other alternatives like itertools (an answer that I think might solve my problem), or using numpy arrays (the problem with this is that my arrays are not homogeneous).

The input list might look like this (3 dimensions):

chords = [[[1, 4, 8, 12], [1, 4, 10, 12]], [[4, 7, 13, 19], [4, 9, 13, 21]]]

My function may generate permutations between two lists:

def combination(list1, list2):
    list = []
    for x in list1:
        for y in list2:
            list.append([x,y])
    return list

combination(chords[0], chords[1])

This function is there for the purpose, but the problem is that, for example, when I introduce combination(combination(chords[0], chords[1]), chords[3])it, this is not calculated separately chords[0]and chords[1](of course, it works as expected).

edit:

Ok, as @iBug pointed out, a good way is to use itertools.product():

bases_chords = [···] #It's a three dimensional array I've filled out  before
possibilities = [] #The list that will contain all the different combinations

for a in product(*bases_chords): #The asterisk means that I input everything on the list
    possibilities.append(a)

print(possibilities)
print(len(possibilities)) #Just to check if the dimensions are right