Question

A student has to answer 6 out of 10 questions which are divided into two parts containing 5 questions each and he is permitted to attempt not more than 4 from any group. In how many ways can he make up his choice?

Answer 1

The different possibilities are mentioned below;

Part I(5)	Part II (5)	Selection of 6
4	2	5C4 x 5C2 = 5C1 x 5C2
3	3	5C3 x 5C3
2	4	5C2 x 5C4 = 5C2 x 5C1

The required number of ways

= 5C₁ × 5C₂ + 5C₃ × 5C₃ + 5C₂ × 5C₁

= 5 × 10 + 10 × 10 + 10 × 5 = 200.