Question

Nadia is picking out some movies to rent, and she is primarily interested in comedies and mysteries. She has narrowed down her selections to 1919 comedies and 88 mysteries.

Step 2 of 2 :  

How many different combinations of 44 movies can she rent if she wants at least one comedy?

Answer 1

Total movies = 19 + 8 = 27

Total number of ways to select 4 movies = 27C4 = 27! / (4! * (27 - 4)!) = 17550

Number of combinations with at least one comedy = total number of combinations - number of combinations with no comedy

                                                                = 17550 - 8C4

                                                                = 17550 - (8! / (4! * (8 - 4)!))

                                                                = 17550 - 70

                                                                = 17480