(a) To open a combination lock, you must know the lock’s three-number sequence in its proper order. Repetition of numbers is permitted. Why is this lock more like a permutation lock than a combination lock? Why is it not a true permutation problem? The order is important. Since the numbers may be repeated, it is not a true permutation lock.

(b) Assuming that a combination lock has 40 numbers, determine how many different three-number arrangements are possible if repetition of numbers is allowed. 

(c) Answer the question in part (b) if repetition is not allowed.

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