A certain four-cylinder combination lock has 45 numbers on it. To open it, you t

Question

A certain four-cylinder combination lock has 45 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 four-number lock combination has been effected. Repetitions are allowed, and any of the 45 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?

Explanation / Answer

Solution:-

a) Different number of lock combinations are 4,100,625.

Number of steps = 4

Total different number that can be used at each step = 45

Different number of lock combinations = 454 = 4,100,625

b) The probability of guessing a lock combination on the first try is 0.000000244.

Number of ways to open lock at first try = 1

The probability of guessing a lock combination on the first try = 1/4100625 = 0.000000244

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