Question

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?

Answer 1

Given as

The total number of questions = 12

The total number of questions to be answered = 7

The number of ways = (No. of ways of answering 5 questions from group 1 and 2 from group 2) + (No. of ways of answering 4 questions from group 1 and 3 from group 2) + (No. of ways of answering 3 questions from group 1 and 4 from group 2) + (No. of ways of answering 2 questions from group 1 and 5 from group 2)

= (⁶C₅ × ⁶C₂) + (⁶C₄ × ⁶C₃) + (⁶C₃ × ⁶C₄) + (⁶C₂ × ⁶C₅)

On using the formula,

ⁿC_r = n!/r!(n – r)!

= (6 × 15) + (15 × 20) + (20 × 15) + (15 × 6)

= 90 + 300 + 300 + 90

= 780

Thus, the total no. of ways of answering 7 questions is 780 ways.