A certain three-cylinder combination lock has 65 numbers on it. To open it, you turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a three-number lock combination has been effected. Repetitions are allowed, and any of the 65 numbers can be used at each step to form the combination. (a) How many different lock combinations are there? (b) What is the probability of guessing a lock combination on the first try?
Accepted Solution
A:
Answer:a) 274,625b) [tex]3.6413*10^{-6}[/tex]Step-by-step explanation:a)
We have an arrangement of 3 numbers (p,q,r) each of them having 65 different possible selections.
By the Fundamental Rule of Counting, there are
65*65*65 = 274,625 different combinations.
b)
Since there is a unique combination which unlocks the device, the probability of guessing it at the first try is
[tex]\bf \frac{1}{274,625}= 3.6413*10^{-6}[/tex]