Out of 19 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 choice from the following:  A) 12â„13  B) 11â„13  C) 10â„15  D) 23/31  E) None of these
Total possible ways of selecting 4 students out of 19 students = 19C4 = 3876   The no. of ways of selecting 4 students in which no student belongs to Karnataka = 14C4=1001   âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 19C4 â€“ 14C4 = 2875   âˆ´ Probability = 2875â„3876 = 23/31   Answer 23/31
<result>D</result>
Out of 19 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?