Question

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?

Answer 1

a) 274,625

b)
`3.6413*10^(-6)`

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

`\bf (1)/(274,625)= 3.6413*10^(-6)`