Question

A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?

Answer 1

Given as

The total number of questions = 10

The questions in part A = 6

The questions in part B = 7

The number of ways = (No. of ways of answering 4 questions from part A and 6 from part B) + (No. of ways of answering 5 questions from part A and 5 questions from part B) + (No. of ways of answering 6 questions from part A and 4 from part B)

= (⁶C₄ × ⁷C₆) + (⁶C₅ × ⁷C₅) + (⁶C₆ × ⁷C₄)

On using the formula,

ⁿC_r = n!/r!(n – r)!

= (15 × 7) + (6 × 21) + (1 × 35)

= 105 + 126 + 35

= 266

Hence, the total no. of ways of answering 10 questions is 266 ways.