more probalility

Question

 There are eight question on a matching test (exactly one answer is paired with one question) . What is the probability that someone who guesses on all five questions will answer them all correctly?

Answer 1

Are there 5 questions or 8 questions?

 

Let's suppose there are 5.  The same idea will work in both cases.

 

Look at the first question.  There are 5 available answers, so the probability that he guesses correctly is 1/5.

 

Now the second question...  There are only 4 available answers left, so the probability that he guesses correctly on this one is 1/4.

 

Similarly, the probability that he guess correctly on the 3rd question is 1/3.

 

Follow this down to the last question.  At that point, there is only one answer left, and if he's guessed correctly on all the others, that must be the correct answer for the last question.

 

Since each guess is an independent event, and he has to guess correctly every time, the probability that he guesses correctly on all of them is (1/5) * (1/4) * (1/3) * (1/2) * (1/1) = 1 / 5!

 

The same is true for 8 questions.  The probability would be 1 / 8!