COMEDK · Maths · 4. Permutation Combination

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?

A 56
B 26
C 27
D 41

Verified Solution

Answer & Solution

Correct Answer

(D) 41

Step-by-step Solution

Detailed explanation

The total number of ways to choose 3 books out of 8 is \(^{8}C_{3} = \dfrac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56\). The condition is that the student cannot borrow Chemistry part 2 (let us call it \(C_2\)) unless he also borrows Chemistry part 1 (\(C_1\)). This means…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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