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

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]