Out of 18 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 answer:
A) 12â„13
B) 11â„13
C) 10â„15
D) 59/77
E) None of these
Total possible ways of selecting 4 students out of 18 students = 18C4 =3060   The no. of ways of selecting 4 students in which no student belongs to Karnataka = 13C4=715   âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 18C4 â€“ 13C4 = 2345   âˆ´ Probability = 2345â„3060= 59/77   Answer 59/77
<result>D</result>
Out of 18 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?