Question 25

# A student is required to answer 6 out of 10 questions in an examination. The questions are divided into two groups, each containing 5 questions. She is not allowed to attempt more than 4 questions from each group. The number of different ways in which the student can choose the 6 questions is

Solution

There are 3 ways in which she can answer the questions:-
1. 3 from group 1 and 3 from group 2
She can select 3 questions from each group in $$^5C_3$$ ways and thus the total number of ways = $$^5C_3*^5C_3$$ = 100
2. 4 questions from group 1 and 2 questions from group 2.
She can select 4 questions from group 1 in 5 ways and 2 questions from group 2 in 10 ways and thus, total number of ways = 50
Same will be the case for 4 questions from group 2 and 2 questions from group 1
Thus, the total number of ways = 100+50+50 = 200
Hence, option C is the correct answer.