A) \[\frac{12}{13}\]
B) \[\frac{11}{13}\]
C) \[\frac{10}{15}\]
D) \[\frac{1}{15}\]
Correct Answer: B
Solution :
Total possible ways of selecting 4 students out of 15 students \[{{=}^{15}}{{C}_{4}}=\frac{15\times 14\times 13\times 12}{1\times 2\times 3\times 4}=1365\] The number of ways of selecting 4 students in which no student belongs to Karnataka \[{{=}^{10}}{{C}_{4}}\] \[\therefore \] Number of ways of selecting atleast one student from Karnataka \[{{=}^{15}}{{C}_{4}}{{-}^{10}}{{C}_{4}}=1155\] \[\therefore \] Required probability \[=\frac{1155}{1365}=\frac{77}{91}=\frac{11}{13}\]
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