about to only mathematics

In a class of 50 students, 35 opted for Mathematics and 37 opted for Biology . How have opted for only Mathematics ? (Assume that each student has to opt for at least one of the subjects )

A school library has 75 books on Mathematics, 35 books on physics. A student can choose only one book , In how many ways a student can choose a book on Mathematics or physics?

In a school there are 30 teachers who teach Mathematics or Physics. Of these teachers, 20 teach. Mathematics and 15 teach Physics, 5 teach both Mathematics and Physics. The number of teaches teaching only Mathematics is:

In a survey of 25 students, it was found that 12 have taken physics, 11 have taken chemistry and 15 have taken mathematics; 4 have taken physics and chemistry; 9 have taken physics and mathematics; 5 have taken chemistry and mathematics while 3 have taken all the three subjects Find the number of students who have taken (i) physics only (ii) chemistry only; (iui) mathematics only (iv) physics and chemistry but not mathematics; (v) physics and mathematics but not chemistry; (vi) only one of the subjects; (vii) at least one of the three subjects; (vii) none of the three subjects.

Among the examinees in an examination, 25%, 30% and 45% failed in statistics, in mathematics and in at least one of statistics and mathematics respectively. An examincee is selected at random. Find the probability that he failed in statistics only.

Among the examinees in an examination, 25%,30% and 45% failed in statistics, in mathematics and in at least one of statistics and mathematics respectively. An examinee is selected at random. Find the probabilities that (i) he failed in statistics only (ii) he passed in statistics if it is known that he failed in mathematics.