The door on the computer center has a lock which has five buttons numbered from 1 to 5. The combination of numbers that opens th
e lock is a sequence of five numbers and is reset every week. (a) How many combinations are possible if every button must be used once?
(b) Assume that the lock can also have combinations that require you to push two buttons simultaneously and then the other three one at a time. How many more combinations does this permit?
