A) \[{{P}_{1}}={{P}_{2}}\]
B) \[{{P}_{1}}>{{P}_{2}}\]
C) \[{{P}_{1}}<{{P}_{2}}\]
D) None of these
Correct Answer: B
Solution :
\[{{P}_{1}}=\frac{{}^{15}{{C}_{2}}\times {}^{27}{{C}_{2}}}{{}^{42}{{C}_{4}}}=\frac{27}{82}\] and \[{{P}_{2}}=\frac{{}^{30}{{C}_{4}}\times {}^{54}{{C}_{4}}}{{}^{84}{{C}_{8}}}=\frac{17\,.\,29\,.\,45\,.\,53}{11\,.\,79\,.\,82\,.\,83}\] (After simplification) Hence \[{{P}_{1}}>{{P}_{2}}.\]
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