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 4 questions from either group. The number of different ways in which the candidate can choose 6 questions is

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 4 questions from either group. The number of different ways in which the candidate can choose 6 questions is (A) 50 (B) 150 (C) 200 (D) 250

Tardigrade Admin · Accepted Answer

The number of ways the candidate can choose questions under the given conditions is enumerated below.

Group 1	Group 2	Number of ways
4	2	$(^{5} C_{4}) (^{4} C_{2}) = 50$
3	3	$(^{5} C_{3}) (^{5} C_{3}) = 100$
5	4	$(^{5} C_{2}) (^{5} C_{4}) = 50$
	Total number of ways	200

Q. 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 $4$ questions from either group. The number of different ways in which the candidate can choose $6$ questions is

$50$

$150$

$200$

$250$

The number of ways the candidate can choose questions under the given conditions is enumerated below.

Group 1 Group 2 Number of ways

4 2 $(^{5} C_{4}) (^{4} C_{2}) = 50$

3 3 $(^{5} C_{3}) (^{5} C_{3}) = 100$

5 4 $(^{5} C_{2}) (^{5} C_{4}) = 50$

Total number of ways 200

Q. 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 4 questions from either group. The number of different ways in which the candidate can choose 6 questions is

50

150

200

250