import math
from tabulate import tabulate

def nth_combination(seq, n):
    #make a copy of seq so we can destroy it without hurting the original
    seq = seq[:]

    result = []
    while seq:
        n, i = divmod(n, len(seq))
        result.append(seq[i])
        del seq[i]
    return result

def nth_product_of_combinations(table, n):
    result = []
    for row in table:
        n, combination_idx = divmod(n, math.factorial(len(row)))
        result.append(nth_combination(row, combination_idx))
    return result

def total_possible_prodcombs(table):
    total = 1
    for row in table:
        total *= math.factorial(len(row))
    return total

table = [[ 'alex', 'smith', 'john'], ['sharlote', 'oliver', 'liam'], ['jasper', 'aria', 'luna']]
for i in range(total_possible_prodcombs(table)): #3! * 3! * 3! == 216
    rearranged_table = nth_product_of_combinations(table, i)
    print(i, rearranged_table)
    print(tabulate(rearranged_table, headers=["A","B", "C"], showindex=range(1,len(table)+1), tablefmt='grid'))