First slide

Combinations

Question

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

Easy

A

80
B

100
C

200
D

None of these

Solution

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

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