SATHEE: Quantitative Aptitude Ques 883

Quantitative Aptitude Ques 883

Question: A basket contains 6 red, 5 green and 8 blue balls. If four balls are picked at random, what is the probability that all four of them are either red or any two out of the four are green?

Options:

A) $ \frac{5}{1292} $

B) $ \frac{925}{3876} $

C) $ \frac{359}{1938} $

D) $ \frac{11}{3876} $

Show Answer

Answer:

Correct Answer: B

Solution:

Total number of balls $ =6+5+8=19 $ Number of ways of selecting 4 balls out of $ 19={{,}^{19}},C _4 $ $ =\frac{19\times 18\times 17\times 16}{1\times 2\times 3\times 4}=3876 $ total number of favorable cases $ ={}^{6}C _4+{}^{5}C _2\times {}^{14}C _2 $ $ =\frac{6\times 5\times 4\times 3}{1\times 2\times 3\times 4}+\frac{5\times 4}{1\times 2}\times \frac{14\times 13}{1\times 12} $ $ =15+(10\times 7\times 13) $ $ =15+910=925 $

$ \therefore $ Required probability $ =\frac{925}{3876} $

Quantitative Aptitude Ques 882

Quantitative Aptitude Ques 884

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