A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borrow Chemistry part 2 unless he can borrow Chemistry part 1 also. In how many ways can he choose the three books to be borrowed?

Step-by-step solution

The total number of ways to choose 3 books out of 8 is ⁸C₃ = 8 7 6 3 2 1 = 56 . The condition is that the student cannot borrow Chemistry part 2 (let us call it C₂ ) unless he also borrows Chemistry part 1 ( C₁ ). This means the only forbidden combination is choosing C₂ while not choosing C₁ . We count the number of forbidden combinations where C₂ is selected but C₁ is not. If C₂ is selected, the student needs to choose 2 more books from the remaining 8 - 2 = 6 books (excluding both C₁ and C₂ ). The number of such