Carcass wrote:

A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?

A 90

B 115

C 130

D 144

E 195

We can break this problem into scenarios:

Scenario 1: 2 biographies and 2 novels

The number of ways to select 2 biographies is 4C2 = 4!/[2! x (4 - 2)! = 4!/(2! x 2!) = (4 x 3)/2! = 6.

The number of ways to select 2 novels is 6C2 = 6!/[2! x (6 - 2)!]= 6!/(2! x 4!) =(6 x 5)/2! = 15.

So there are a total of 6 x 15 = 90 ways for this scenario.

Scenario 2: 3 biographies and 1 novel

The number of ways to select 3 biographies is 4C3 = 4.

The number of ways to select 1 novels is 6C1 = 6.

So there are a total of 4 x 6 = 24 ways for this scenario.

Scenario 3: 4 biographies

The number of ways to select 4 biographies is 4C4 = 1.

So there is only 1 way for this scenario.

So there are a total of 90 + 24 + 1 = 115 ways to choose 4 books that consist 2 or more biographies.

Answer: B

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