A door lock is opened by pushing a sequence of buttons. Each of the three terms in the combination is entered by pushing either one button or two buttons simultaneously. If there are 5 buttons, how many diﬀerent combinations are there? (Example: 1-3, 2, 2-4 is a valid combination.)

Question

Quizplus · Accepted Answer

The Answer is A push of buttons in the combinations is either the push of one of the five buttons or the simultaneous push of one of

C ( 5,2 ) = 10

combinations of two of the five buttons. Hence there are

15 \cdot 15 \cdot 15 = 3375

possible combinations for the door lock.

A Door Lock Is Opened by Pushing a Sequence of Buttons