C(x,y) stands for the total number of combinations possible drawing y cards out of x total cards. It is an Excel function COMBIN, or can be calculated from Factorials or manually when y is small. The formula is x!/(y!*(x-y)!). For example for your pockets its C(52,2)=52!/(50!*2!). Note that since y is small, almost all of the 52! is cancelled out by the 50!, so all that is left is 52*51/2=1326, the number of possible pocket cards you could have.
Your problem requires several different steps to determine whether the Qs hold up when you consider the long shot hands such as 4 of one of your suits and no one else having them, making a straight that doesnt stretch to the AA, etc. The majority of times it holds up, though, it will be because no A or K appears on the board, and is a close enough approximation. That would be calculated vs AA for example, as C(46,5)/C(48,5). In English, the total number of combinations for the board is 5 cards out of the 48 unknown (after the QQAA). The winning combinations are 5 cards out of the 46 after removing the other two Aces.
You would get the same for the KK. For AK you have to remove 6 cards from the deck instead of just 2, so it becomes C(42,5)/C(48,5).
When it gets as complex as finding the complete answer, you are far better off using software that does it for you. Ive seen
www.twodimes.net recommended here, but I dont like it. I use Hold'em Analyzer, but its not free.