A) \[\frac{231}{646}\]
B) \[\frac{274}{637}\]
C) \[\frac{215}{615}\]
D) \[\frac{240}{637}\]
E) \[\frac{165}{646}\]
Correct Answer: E
Solution :
Total number of students\[=12+8=20\] \[\therefore n(S){{=}^{2n}}{{C}_{5}}=\frac{20\times 19\times 18\times 17\times 16}{5\times 4\times 3\times 2\times 1}=15504\] \[n(E){{=}^{12}}{{C}_{4}}{{\times }^{8}}{{C}_{1}}\] \[=\frac{12\times 11\times 10\times 9}{1\times 2\times 3\times 4}\times 8=455\times 8=3960\] \[\therefore P(E)=\frac{n(E)}{n(S)}=\frac{3960}{15504}=\frac{165}{646}\]
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