May 2016 Problem

Ten students are standing in line. How many possibilities do we have to select four out of them, so that no two were neighbors in this line?

Dear friends of the site, as usually, there were many answers, though not of them correct. Probably, the problem seemed to you more difficult than the previous one. The first to submit correct answers were Alexander, David and Hyun-Woo. Congratulations to them and many thanks to all the participants.                                                                   Here is my solution: Simple analysis shows that the problem can be reduced to the following: calculate the number of possibilities to choose 4 objects among 7, in other words, 7C4 = 35.