A question paper is divided into two parts A and B and each part contains 5 questions. The number of ways in which a candidate can answer 6 questions selecting atleast two questions from each part is

# A question paper is divided into two parts A and B and each part contains 5 questions. The number of ways in which a candidate can answer 6 questions selecting atleast two questions from each part is

1. A

80

2. B

100

3. C

200

4. D

None of these

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### Solution:

The number of way6 that the candidate may select
(i) if 2 questions from. A and 4 questions from B ${=}^{5}{\mathrm{C}}_{2}{×}^{5}{\mathrm{C}}_{4}=50$
(ii) 3 questions from A and 3 questions from B ${=}^{5}{\mathrm{C}}_{3}{×}^{5}{\mathrm{C}}_{3}=100$
(iii) 4 questions from 4 and 2 questions from B ${=}^{5}{\mathrm{C}}_{4}{×}^{5}{\mathrm{C}}_{2}=50$
Hence, total number of ways = 50 + 100 + 50 = 200

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