There are two groups of subjects, one of which consists of 5 science subjects and 3 Engineering subjects and the other consists of 3 science and 5 Engineering subjects. An unbiased die is cast. If number 3 or 5 turns up, a subject from 1 is selected otherwise a subject is selected from group 2. The probability that an Engineering subject is selected ultimately, is

In a group of 1300 students every student reads 5 subjects and every subject is read by 65 students. The number of subjects are :

In how many ways can 5 subjects be chosen from 9 subjects if three subjects are compulsory?

A group of 50 students appeared for the two examinations one in Physics and the other in Mathematics. 38 students passed in Physics and 37 in Mathematics. If 30 students passed in both subjects, determine how many students failed in both the subjects.

For a group of students,30%,40% and 50% failed in Physics,Chemistry and at least one of the two subjects respectively.If an examinee is selected at random,what is the probability that he passed in Physics if it is known that he failed in Chemistry?

There are six teachers A, B, C, D, E and F in a school. Each of the teachers teaches two subjects, one compulsory subject and the other optional subject. D's optional subject is History while three others have it as compulsory subject. E and F have Physics as one of their subjects. F's compulsory subject is Mathematics which is an optional subject of both C and E. History and English are A's subjects but in terms of compulsory and optional subjects, they are reverse of those of D's. Chemistry is an optional subject of any one of them. There is only one female teacher in the school who has English as her compulsory subject. Which of the following groups of teachers has History as the compulsory subject ?