Q. On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done? Published on 07 Jul 17
Answer is : 2880
Answers
There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways.
Further, in each category (subject), books are to be arranged in different order, we get,
Required number of ways:
3! * [2! * 2! * 5!] = 2880
The total ways are 2880.
Given,
The number of books of Geology = 2
The number of books of Sociology = 2
The number of books of Economics = 5
To Find,
The number of ways to arrange books such that the books of any subject are to be together =?
Solution,
The books are to be arranged in such a way that the books of any subject are to be together. That means we have to arrange 3 subjects.
The number of ways to arrange books of 3 subjects = 3! = 3*2*1
The number of ways to arrange books of 3 subjects = 6 ways
The number of ways to arrange 2 books of Geology = 2! = 2*1
The number of ways to arrange 2 books of Geology = 2 ways
The number of ways to arrange 2 books of Sociology = 2! = 2ways
The number of ways to arrange 5 books of Economics = 5!
The number of ways to arrange 5 books of Economics = 5*4*3*2*1
The number of ways to arrange 5 books of Economics = 120 ways
Total ways = (Number of ways to arrange 3 subjects)*(Number of ways to arrange books of all subjects)
Total ways =(6)*(2*2*120)
Total ways = 2880
Hence, the number of ways to arrange books such that the books of any subject are to be together is 2880 ways.