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 counterclockwise to a number, then rotate clockwise to a second number, and then counterclockwise to the third number and so on until a four-number lock combination has been effected. Repetitions are allowed. (a) How many different lock combinations are there? (b) What is the probability of guessing a lock combination on the first try? The number of different four-number lock combinations is. (Type an integer or fraction. Simplify your answer.) The probability that the correct lock combination is guessed on the first try is. (Type an integer or fraction. Simplify your answer.)

Explanation / Answer

Part (a)

The first number can be any one of the 45 numbers. Since repetition is permitted, the same number can come again. So, the second number also can be any one of the 45 numbers. By the same logic, the third and the fourth numbers can also be any one of the 45 numbers. Thus, total number of combinations possible is 454

= 4100625 ANSWER

Part (b)

Out of 4100625 possible combinations, only one combination is correct. Hence, probability of the correct combination in the very first try = 1/4100625 = 0.0000002439 ANSWER

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