The problem is a classic one of mixing cin >> and getline( cin, std::string )
cin >> leaves the newline character '\n' in the stream ... and this will be picked up as a blank by the following getline().
getline() extracts (and throws away) the newline character.
There are lots of ways round this; here are four of them
(1) Don't mix them: use getline for everything. e.g.
getline( cin, dummy ); stringstream( dummy ) >> Number_Of_Students;
(2) After any use of cin >> use cin.ignore to extract up to the newline character (1000 ought to be more than enough):
cin >> Number_Of_Students; cin.ignore( 1000, '\n' );
(3) After any use of cin >> use a getline with a redundant string just to pick up any trailing blanks and the newline:
cin >> Number_Of_Students; getline( cin, dummy );
(4) Clear any preceding whitespace at the following getline call:
getline(cin >> ws, student[x].name);
(This is slightly dangerous as it is not local to the problem - you might decide to rearrange your input.)
Take your pick. There are probably plenty more ways of solving the problem. Method (2) seems to be the most used in this forum, but I've used all of them at one time or another.
BTW, your questions would be much easier to answer if you used code tags (first item in the format menu - you can edit a post if it doesn't appear on the initial posting.)
Also, your title doesn't have much to do with the problem.