Some doors on cars can be opened by pressing a correct sequence of buttons. A display of the five buttons by the door handle of a car follows.

On most cars, although each key lists two numbers, the key acts as a single number. Therefore, if your code is 1, 6, 8, 5, 3, the code 2, 5, 7, 6, 4 will also open the lock.

The correct sequence of five buttons must be pressed to unlock the door.

(a) How many different sequences of five buttons are possible (repetition is permitted)? 

(b) If a sequence of five buttons is pressed at random, determine the probability that the sequence unlocks the door.

Transcribed Image Text:

9 -0 7-8 3 - 4 5 -6 1-2