A certain fourfour?-cylinder combination lock has 5555 numbers on it. To open? i

Question

A certain

fourfour?-cylinder

combination lock has

5555

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

fourfour?-number

lock combination has been effected. Repetitions are? allowed, and any of the

5555

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?

?(a) The number of different

fourfour?-number

lock combinations is

nothing.

?(Type an integer or fraction. Simplify your? answer.)

?(b) The probability that the correct lock combination is guessed on the first try is

nothing.

?(Type an integer or fraction. Simplify your? answer.)

Explanation / Answer

SINCE QUESTION IS NOT DISPLAYED PROPERLY, I AM ASSUMING 4 CYLINDERS AND 55 NUMBERS ON IT

(a)

choices for the first cylinder 55

choices for the second cylinder is again 55

for the third cylinder, you have 55 choices .

And for the fourth cylinder, you have 55 choices again.

So the answer is going to be 55*55*55*55, or 554  = 9150625

(b) first number correct=1/55=second number correct=third correct =fourth correct

So (1/55)^4 = 1/554

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