There are five distinct computer science books three distinc

There are five distinct computer science books, three distinct mathematics books, and two distinct art books. In how many ways can these books be arranged on a shelf if one of the mathematics books is on the left of all computer science book, and another mathematics book is on the right of all the computer science books?

Solution

number of cs books = 5

maths books = 3

art books = 2

so total there are 10 books

now there are 10 places to keep a book

Place the art books in one of 109 ways.

[as there are 2 aart books 1st book can be placed in sny of 10 places and coming to the 2nd there are only 9 places lefft as 1 place is already occupied]

now we are having 8 empty places and 8 books

We can order the five CS books among themselves in 5! ways and

maths books in 3! ways

Put M1 to the left of the CS books and M3 to the right of the CS books. Choose one of the 6 slots so created for M2.

and now total is

10*9*6*5!*3! = 38880 ways