# what's the probability?

I have 2 Lists A & B , each list has 10 elements which related to others , what If I want to cross a line between the elements , each element in A has 1 correct answer in B . what's the probability that my answer will be correct 100%?

• At least three people (Cameron, Parth, and I) interpret the question in exactly the same way, two of us before the question was put ‘on hold’. It appears that we have some over-hasty closers in action here. – Brian M. Scott Jul 11 '13 at 19:25
• @BrianM.Scott I'll vote for you on the next election. – Git Gud Jul 11 '13 at 20:06

There is just one correct way of matching the items. But there are $10!$ possible ways to match the items (why?). So the answer is $\dfrac 1 {10!}$
Well, just go down the list. How many possible matchups (correct or incorrect) are there for the first item in $A$? Once we've chosen a match for that one, how many are left to potentially match up with the second item in $A$? Once we've matched that one, how many ways can we pick a match for the third? (Continue in this fashion, and use Counting Principle.)