Question

There are 6 books on Economics, 3 on Mathematics and 2 on Accountancy. In how many ways can these be
placed on a shelf if the books on he same subject are to be together?
(a) 51840
(b) 51880
(c) 51860
(d) None




question of Permutation ​

Answer 1

GIVEN :

There are 6 books on Economics, 3 books on Mathematics and 2 books on Accountancy. In how many ways can these books be  placed on a shelf if the books on the same subject are to be together?

(a) 51840

(b) 51880

(c) 51860

(d) None

TO FIND :

In how many ways can these books be  placed on a shelf if the books on the same subject are to be together.

SOLUTION :

Given that there are 6 books on Economics, 3 books on Mathematics and 2 books on Accountancy.

We know the formula $n!=n(n-1)(n-2)...3.2.1$

Now arranging the books on the shelf as below :

Economics = 6! = 720

Maths = 3! = 6

Accountancy = 2! =2

Thus, the total number of arranging the books on the same subject are to be together in the shelves are 3! =6

Thus, total number of ways arrangement is

$6! \times 3! \times 2! \times 3!=720\times 6\times 2\times 6$

= 51840

$6! \times 3! \times 2! \times 3!= 51840$

Option a) 51840 is correct

∴ 51840 ways the books on the same subject are to be together can be  placed on a shelf.