Suppose that two engineering, four computer science, three statistics, three biology, and five music books are put on a bookshelf with a random arrangement. What is the probability that the books of the same subject are together?

Step-by-step explanation:

Here we have 5 groups of books from 5 different subjects, but, those groups consists of different number of books and they must be arranged together.

We can arrange them on the following way:

2 Engineering =2!

4 Computer Science =4!

3 Statistics =3!

3 Biology =3!

5 Music books =5!    

But, also, those 5 groups can change their places and they can be arranged on 5! ways, so we can arrange them on 5!2!4!3!3!5! ways.

But, required probability will be:

because we have in total 17 books.

see below

Step-by-step explanation:

Let's solve for x first. Since opposite sides of a parallelogram are congruent, 5x = 5 which means x = 1. Similarly, opposite angles of a parallelogram are congruent so m∠X = m∠V = 107°. Since ∠YWV and ∠XYW are alternate interior angles, that means that ∠XYW = 42°.