In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?

A class has 175 students. The following data shows the number of students obtaining one or more subjects : Mathematics 100 , Physics 70 , Chemistry 40 , Mathematics and Physics 30 , Mathematics and Chemistry 28 , Physics and Chemistry 23 , Mathematics & Physics & Chemistry 18 . How many students have offered Mathematics alone ?

There are four teachers and five classes in a school. One teacher teaches only one class at a time. In how many ways can the teachers choose the classes?

The sum of the costs of one book each of Mathematics, Physics and Chemistry is Rs 210. Total cost of a mathematics book, 2 physics books, and a chemistry book is Rs. 240/- Also the total cost of a Mathematics book, 3 physics book and 2 chemistry books is Rs. 300/-. Find the cost of each book using matrices.

The chances to fail in Physics are 20% and the chances to fail in Mathematics are 10%. What are the chances to fail in atleast one subject ?