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.


(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?
~~~~~~~~~~~~~~~~~~


<pre>
(a)  <U>ANSWER</U>.  There are  {{{14^4}}} = 38416  different combinations.


     <U>Explanation</U>.  There are 14 independent options in each of 4 positions.



(b)  <U>ANSWER</U>.   Probability  P = {{{1/14^4}}}.


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



(c)  <U>ANSWER</U>.  {{{25/14^4}}}.
</pre>

Answered, solved, explained and completed.