Amy plans to put a total of eight books on her shelf She has

Amy plans to put a total of eight books on her shelf. She has seven different textbooks and seven different fiction novels. The shelf should contain at least four of the textbooks and at least two of the novels. How many ways can she select eight books to go on the shelf?

Solution

1. 4 Txtbooks 4 novels: 7C4*7C4 = 35*35 = 1225

2. 5 Txtbooks 3 novels: 7C5*7C3 = 21*35 = 735

3. 6 Txtbooks 2 novels: 7C6*7C2 = 7*21 = 147

Total ways = 1225+735+147= 2107