Question

A candidate is required to answer 6 out of 12 questions which are divided into two parts A and B, each containing 6 questions and he/she is not permitted to attempt more than 4 questions from any part. In how many different ways can he/she make up his/her choice of 6 questions ?

• A. 850
• B. 800
• C. 750
• D. 700

Answer 1

Answer: (A)

850

Answer 2

$A\,\,\,B$
$4\,\,\,2\,\,\,\to\,\,\,^{6}C_{4} \times \,^{6}C_{2}$
$2\,\,\,4\,\,\,\to\,\,\,^{6}C_{2} \times \,^{6}C_{4}$
$3\,\,\,3\,\,\,\to\,\,\,^{6}C_{3} \times \, ^{6}C_{3}$
Total $2\times \, ^{6}C_{2}\times \, ^{6}C_{4}\times \, ^{6}C_{3}\times \, ^{6}C_{3} = 450 + 400 = 850$