Question

A candidate is required to answer 6 out of 10 questions which are divided into two groups ,each containing 5 questions. he is not permitted to attempt more than four questions from either group.THe number of different ways in which the candidate can choose six questions

Answer 1

First, notice that since he can choose atmost 4 questions from one group,
he needs to choose atleast 2 questions frome each group

Answer 2

That gives us 3 cases to work with :


first group : 4 questions
second group : 2 questions

first group : 3 questions
second group : 3 questions

first group : 2 questions
second group : 4 questions

Answer 3

for the first case :
you can choose 4 questions from the available 5 questions in 5C4 ways
you can choose 2 questions from the available 5 questions in 5C2 ways

So the total number of ways of answering 4 questions from first group and 2 questions from second group would be : 5C4*5C2

Answer 4

see if you can work the remaining cases similarly

Answer 5

ok thanks