4. corrupt professor z has a class of 50 students. he needs to give exactly 10 a's. however five students already have a special deal (they are professor z's nephews and nieces) and will get a's for sure. how many ways can the 10 a's be distributed?

Step-by-step explanation:

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

i.e. 45P5 ways

no of ways = 45P5 == 146611080

the answer is (x−3)(x−9)