Student scores zero on matching section

The Spanish teacher at my school showed me a test that was divided into various sections. Some matching, some fill-in-the-blank, some word banks, etc. Somehow, this student scored a zero on the entire test. What struck me is that they were very unlucky to get nothing right in any section, but it made me think of this question specifically:

In a matching section of a test, with 7 questions and 7 answers, what are the chances of getting exactly zero correct when choosing randomly?

I feel like I should be able to answer this question on my own, but am not sure where to start. Depending on the first few choices made, it can make it either impossible or 100% certain that a right answer may fall on the last choice(s).

About 36.79%.

You're looking for "derangements," the number of permutations of a list where no item is in its original position. Coincidentally, the example given on Wikipedia also involves test taking:
http://en.wikipedia.org/wiki/Derangement.

I thought the answer was (6/7)^7 = 33.9917%

Quote: boymimbo

I thought the answer was (6/7)^7 = 33.9917%

That would be the case if each answer was independent. You could potentially "force" a correct answer even though the first 6 were wrong.

I guess you could also have an exceptionally..talented...student who matches an answer to a question more than once...

Oh, it's a matching problem. As Emily Litella would say, "never mind".