Question

A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two question from each section among 6 questions he answers. How many different choices does the student have in choosing questions?

Answer 1

There are 11 questions, out of which 5 questions are from section I and 6 questions are from section II.

The student has to select 6 questions taking at least 2 questions from each section.

Consider the following table:

	Case I	Case II	Case III
No. of questions	Sec I (2Q) Sec II (4Q)	Sec I (3Q) Sec II (3Q)	Sec I (4Q) Sec II (2Q)
Number of ways	5C2 × 6C4 = 10 × 15 = 150	5C3 × 6C3 = 10 × 20 = 200	5C4 × 6C2 = 5 × 15 = 75

∴ Number of choices = 150 + 200 + 75 = 425

∴ In 425 ways students can select 6 questions, taking at least 2 questions from each section.