In an exam, a student has to answer 10 questions out of 12. It is mand

1.	In an exam, a student has to answer 10 questions out of 12. It is mandatory to answer 4 questions from section A and 5 questions from section B. If both sections have an equal number of questions, in how many ways can the student attempt the paper?1. 782. 513. 424. 30
Answer» Correct Answer - Option 2 : 51 Concept: The ways of arranging n different things = n! The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\) The no. of ways of arranging the n arranged thing and m arranged things together = n! × m! The number of ways for selecting r from a group of n (n > r) = nCr Calculation: Each section has 6 questions The selection can be done in the following ways = (4 from section A and 6 from section B) or (5 from each section) Ways of selecting 4 questions out of 6 from section A = 6C4 = 15 Ways of selecting 5 questions out of 6 from section A = 6C5 = 6 Ways of selecting 5 questions out of 6 from section B = 6C5 = 6 Ways of selecting 6 questions out of 6 from section B = 6C6 = 1 Hence number ways N = 15 × 1 + 6 × 6 = 51 ways

In an exam, a student has to answer 10 questions out of 12. It is mandatory to answer 4 questions from section A and 5 questions from section B. If both sections have an equal number of questions, in how many ways can the student attempt the paper?1. 782. 513. 424. 30

Answer» Correct Answer - Option 2 : 51

Concept:

The ways of arranging n different things = n!
The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\)
The no. of ways of arranging the n arranged thing and m arranged things together = n! × m!
The number of ways for selecting r from a group of n (n > r) = nCr

Calculation:

Each section has 6 questions

The selection can be done in the following ways = (4 from section A and 6 from section B) or (5 from each section)

Ways of selecting 4 questions out of 6 from section A = 6C4 = 15

Ways of selecting 5 questions out of 6 from section A = 6C5 = 6

Ways of selecting 5 questions out of 6 from section B = 6C5 = 6

Ways of selecting 6 questions out of 6 from section B = 6C6 = 1

Hence number ways N = 15 × 1 + 6 × 6 = 51 ways