SOLUTION: The combination bike lock has four wheels, each of which has the numbers 0 through 13. Exactly one combination of numbers (in order) on the wheels (7-2-10-6,) will open the lock.

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Question 1139207: The combination bike lock has four wheels, each of which has the numbers 0 through 13. Exactly one combination of numbers (in order) on the wheels (7-2-10-6,) will open the lock.
How many possible combinations of numbers are there on my bike lock?
Suppose that I have forgotten my combination. At random I try 1-2-3-4. What is the probability that the lock will open with this combination?
I try at random 25 different combinations. What is the probability that 1 of these 25 efforts will open the lock?
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
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The combination bike lock has four wheels, each of which has the numbers 0 through 13.
Exactly one combination of numbers (in order) on the wheels (7-2-10-6,) will open the lock.

(a) How many possible combinations of numbers are there on my bike lock?

(b) Suppose that I have forgotten my combination. At random I try 1-2-3-4. What is the probability that the lock will open with this combination?

(c) I try at random 25 different combinations. What is the probability that 1 of these 25 efforts will open the lock?
~~~~~~~~~~~~~~~~~~ 

(a)  ANSWER.  There are   = 38416  different combinations.


     Explanation.  There are 14 independent options in each of 4 positions.



(b)  ANSWER.   Probability  P = .


     It is true for the combination 1-2-3-4, as well for any other fixed combination.



(c)  ANSWER.  .

Answered, solved, explained and completed.


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