Given that the professor Z has a class of 50 students is corrupt. However five students already have a special deal (they are professor Z's nephews and nieces) and will get A's for sure.
Thus out of 10 students 5A's are reserved
Remaining 5 can be distributed in
I 5 to any one of the 45, II to any one of the 44....
and 
, then 
, we get
