Question

Shaun is picking out some movies to rent, and he is primarily interested in documentaries and mysteries. He has narrowed down his selections to 12 documentaries and 19 mysteries. Step 2 of 2 : How many different combinations of 4 movies can he rent if he wants at least one documentary?

Answer 1

31465

Explanation:

31C4=31465

Answer 2

The total number of combinations in which the movies can be rented such that there is at least one documentary is 27589.

Explanation:

The total movies are given as 19 mysteries +12 documentaries=19+12=31

Now the number of total combinations such that 4 movies are rented is given as
`^(31)C_4=31465`

Now the number of total combinations with no documentary is given as

`^(19)C_4=3876`

So the number of combination such that at least one movie is documentary is given as

=Total Combinations-Combinations with no documentary

=31465-3876

=27589

So the total number of combinations in which the movies can be rented such that there is at least one documentary is 27589.