permutations

permutations = []
letters = ['a','b','c']

def find_permutations(config):
    successors = get_successors(config)
    for successor in successors:
        if (len(successor) == 3):
            permutations.append(successor)
        find_permutations(successor) # still find the successors


def get_successors(config):
    successors = []
    for letter in letters:
        if (letter not in config):
            successors.append(config+letter)
    return successors

##other solution:

def backtracking(config, options):
    if len(config) == len(options): # add to array
        permutations.append(config[:])
    else:
        for option in options: # get the sucessors and backtrack them
            if option in config:
                continue
            config.append(option)
            backtracking(config, options)
            config.pop() # for new config


# run
backtracking([], letters)
find_permutations('')
print(permutations)