There are 22 files. If there are a total of 7 that are corrupt, how many sets of 5 will contain exactly 2 corrupt files?

Question

mythorius · Answer

4 sets of 5 will contain 2 corrupt files, the last set will only contain 1. I think

faiqraees · Answer

After every 2 files a corrupt file will come
NNCNNCNNCNNCNNCNNCNNCN
Now Make sets of 5
NNCNN CNNCN NCNNC NNCNN CN

N means not corrupt C means corrupt

anonymous · Answer

After every 2 files a corrupt file will come? Where does this come from?

anonymous · Answer

Who is to say the files couldn't be like so: CCCCNNNNNNNNCCNNNCNNNN  ?
Then if I make sets of 5, I get something like.. {CCCCN, NNNNN, NNCCN, NNCNN, NN} where only one set contains exactly 2 corrupt.

mythorius · Answer

It's not asking it that way, it's asking if you were to put them evenly in each set of five, how many sets of five would two corrupt files be in. Does that help you understand?

anonymous · Answer

I don't understand how it is asking that way, no. All I know from the problem the way it is written is:
- There are 22 files.
- 7 of those 22 are corrupt.
- We are splitting the 22 into sets of 5. There are a lot of ways to do this. (22 choose 5 = 26334)

Then we are being asked, of those ways of making 5, how many will contain 2 corrupt files?

anonymous · Answer

I feel like the problem with your answer is that you are assuming something that is not given in the problem.. that the files are placed in some order, or that we are picking sets of 5 in clumps of 5. What if I pick one from each end to form my sets of 5?

mythorius · Answer

Okay, @jdc1980  The question is talking rationally. You, my friend, are thinking irrationally about how the question could be asked. I only assume because that's the way I was taught how to do math.

bobo-i-bo · Answer

Another way to phrase the question is: how many combinations of 2 corrupt and 3 non-corrupt files can I have?