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  4. Six distinct numbers are chosen from the first 10 natural numbers. The probability that 6 is the third largest of those chosen numbers, is

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Q. Six distinct numbers are chosen from the first $10$ natural numbers. The probability that $6$ is the third largest of those chosen numbers, is

NTA AbhyasNTA Abhyas 2020Probability

Solution:

Total cases = $\_{}^{10}C_{6}^{}$
Favourable cases = $^{4}C_{2}^{}\cdot ^{1}C_{1}\cdot ^{5}C_{3}$
Required probability = $\frac{^{4}C_{2}^{} \cdot ^{1} C_{1} \cdot ^{5} C_{3}}{\_{}^{10}C_{6}^{}}=\frac{2}{7}$