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 at least one is from Karnataka? Choose the correct option.
A) 12⁄13
B) 11⁄13
C) 10⁄15
D) 1⁄15
E) None of these
Total possible ways of selecting 4 students out of 15 students = 15C4 = 15×14×13×12 /1×2×3×4=1365   The no. of ways of selecting 4 students in which no student belongs to Karnataka = 10C4   ∴ Hence no. of ways of selecting at least one student from Karnataka = 15C4 – 10C4 = 1155   ∴ Probability = 1155⁄1365 = 77⁄91 = 11⁄13   Answer 11⁄13
<result>B</result>
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 at least one is from Karnataka?