Question

A certain question paper contains three parts A, B, C with four questions in part $A$, five questions in part $B$ and six questions in part C. A student is required to answer seven questions choosing at least two questions from each part. Then the total number of different ways a student can choose his seven questions for answering, is

• A. 1500
• B. 1200
• C. 1900
• D. 2700

Answer 1

Answer: (D)

In question paper contain three parts $A, B$ and $C$ having $4,5$ and $6$ question respectively.
Total number of way of answering $7$ question in which atleast two question each is
$\Rightarrow { }^{4} C_{3} \times{ }^{5} C_{2} \times{ }^{6} C_{2}+{ }^{4} C_{2} \times{ }^{5} C_{3} \times{ }^{6} C_{2}+{ }^{4} C_{2} \times{ }^{5} C_{2} \times{ }^{6} C_{3}$
$\Rightarrow 4 \times 10 \times 15+6 \times 10 \times 15+6 \times 10 \times 20$
$\Rightarrow 600+900+1200=2700$