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

Moderate

Solution

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

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