SOLUTION: Hi can someone help me solve this please? I got the first answer right on figuring out how many possible combinations of numbers there were on the lock but I am struggling with fig

Question 1139895: Hi can someone help me solve this please? I got the first answer right on figuring out how many possible combinations of numbers there were on the lock but I am struggling with figuring out the answers to b and c. Thanks.
My combination bicycle 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, e.g.) will open the lock.
How many possible combinations of numbers are there on my bicycle 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? (Enter your probability as a fraction.)

(c) Out of frustration I try at random 25 different combinations. What is the probability that 1 of these 25 efforts will open the lock? (Enter your probability as a fraction.)

Answer by ikleyn(52754) (Show Source): You can put this solution on YOUR website!
.

(a)  The total number of all possible combinations of numbers in this case is   = 38416.

     It is because there are 14 possible independent opportunities in each of 4 positions.



(b)  The probability that every (any) fixed concrete combination will open the lock is therefore   = .

     The probability that the combination {1-2-3-4} is the happy key is therefore also   = .



(c)  If you try 25 different combinations of 4 numbers, the probability to open the lock is   = .

I answered ALL YOUR QUESTIONS.

Do not forget to post your "THANKS" to me immediately after reading my post.

/\/\/\/\/\/\/\/\/

By the way, this problem came to the forum some days ago, and I answered and solved it under this link

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1139207.html

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1139207.html

What is or what was the need to post it again ?

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