CLAT Sample Paper CLAT Sample Paper-8

  • 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)         \[\frac{1}{15}\]                        

    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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