Four cards are drawn from a pack of 52 cards. The probability of getting exactly two…

Mathematics · JEE Main · NTA Exams — Statistics and Probability

Four cards are drawn from a pack of 52 cards. The probability of getting exactly two kings and two clubs is

\(\frac{{ }^{3} c_{2} \cdot{ }^{12} c_{2}+{ }^{3} c_{1} \cdot{ }^{12} c_{1} \cdot{ }^{3} c_{2}}{{ }^{52} c_{4}}\)
\(\frac{{ }^{3} c_{2} \cdot{ }^{12} c_{2}+{ }^{3} c_{1} \cdot{ }^{12} c_{1} \cdot{ }^{36} c_{1}}{{ }^{52} c_{4}}\)
\(\frac{{ }^{3} c_{2} \cdot{ }^{13} c_{2}+{ }^{3} c_{1} \cdot{ }^{12} c_{1} \cdot{ }^{36} c_{2}}{{ }^{52} c_{4}}\)
\(\frac{{ }^{4} c_{2} \cdot{ }^{13} c_{2}+{ }^{3} c_{1} \cdot{ }^{12} c_{1} \cdot{ }^{36} c_{2}}{{ }^{52} c_{4}}\)

Answer

(C) ^ 3 c_ 2 ^ 13 c_ 2 + ^ 3 c_ 1 ^ 12 c_ 1 ^ 36 c_ 2 ^ 52 c_ 4

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