Permutations And Combinations Question 175

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

Options:

A) 50

B) 150

C) 200

D) 250

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c] 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