• question_answer Out of 15 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa Four students are to be selected at random. What are the chances that atleast one is from Karnataka? A)  $\frac{12}{13}$                                   B)  $\frac{11}{13}$                       C)  $\frac{10}{15}$                       D)         $\frac{1}{15}$

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 $=\frac{1155}{1365}=\frac{77}{91}=\frac{11}{13}$