In MOCK CAT, Quantitative Aptitude section was divided into 3 groups of 5, 5 and 4 questions respectively. A candidate is required to answer 6 questions taking at least two question from each of the first two groups and at least one question from the third group. In how many ways can he make up his choice?

1200

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1400

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1284

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1560

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Solution

The correct option is B 1400
Required number of ways
$= (^{5} C_{2} \times^{5} C_{3} \times^{4} C_{1}) + (^{5} C_{3} \times^{5} C_{2} \times^{4} C_{1}) + (^{5} C_{2} \times^{5} C_{2} \times^{4} C_{2}) = (10 \times 10 \times 4) + (10 \times 10 \times 4) + (10 \times 10 \times 6) = 1400$

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The correct option is B 1400Required number of ways =(5C2×5C3×4C1)+(5C3×5C2×4C1)+(5C2×5C2×4C2)=(10×10×4)+(10×10×4)+(10×10×6)=1400

The correct option is B 1400
Required number of ways
$= (^{5} C_{2} \times^{5} C_{3} \times^{4} C_{1}) + (^{5} C_{3} \times^{5} C_{2} \times^{4} C_{1}) + (^{5} C_{2} \times^{5} C_{2} \times^{4} C_{2}) = (10 \times 10 \times 4) + (10 \times 10 \times 4) + (10 \times 10 \times 6) = 1400$