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The door on the computer center has a lock which has five buttons numbered from 1 to 5.
The combination of numbers that opens the lock is an ordered 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 simultaneously. How many combinations does this permit?
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(a) How many combinations are possible = 5*4*3*2*1 = 5! = 120. ANSWER
(b) In this case, the description is not clear.
It can be understood by two different ways.
One way is to select first two buttons and push them simultaneously; then to push simultaneously
the remaining three buttons.
In this way, there are = = = 10 possible different choices.
Another way is to select first two buttons and push them simultaneously; then to push simultaneously
any other three buttons, not necessary the remaining buttons.
In this way, there are = 10*10 = 100 possible different choices.
Solved, answered and explained.