problem GRE combination

Question

The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR? I don't know about right answer, but it may be...The order of each letter in the dictionary is ABLORU. Now, with A in the beginning, the remaining letters can be permuted in 5! ways. Similarly, with B in the beginning, the remaining letters can be permuted in 5! ways. With L in the beginning, the first word will be LABORU, the second will be LABOUR

Answer 1

The 6 letters are different. Thus, you need to do a permutation here: picking all 6 when the order matters.

6!/(6-6)! = 6!/0! = 6!/1 = 6*5*4*3*2*1 = 720