For the answer to your second question (the one with the attachment);

It's 16P2 - 16 = 16!/14! - 16 = 240 - 16 = 224

Now 16P2 is essentially the total number of ways in which mike and the other guy can be arranged. 16 ways is the number of ways in which they ALWAYS sit across each other. There are 5 + 3 possibilities where Mike takes his seat first and Jordan sits across. There are then 5 + 3 possibilities when Jordan sits first and Mike sits across. Hence 5+3+5+3 = 16.

Now for your first question, I don't think that's the entire question. It's probably what is the minimum value of n for which n! = 1*2*....*n is a multiple of 990. In which case the answer is 11.