Question

There are $6$ books of Economics, $3$ of Mathematics and $2$ of Accountancy. In how many ways can these be placed on a shelf, if:
1. Books on the same subject are together ?
2. Books on the same subject are not together ?

Answer 1

For 1:

We have $6$ books of Economics, $3$ of Mathematics and $2$ of Accountancy

Arranging the books within the branches:

Economics - $6!$

Maths - $3!$

Accountancy - $2!$

Thus the arranging branches are $3!$

Thus, total arrangement

$6!\times 3!\times 2!\times 3!=32,400$

For 2: We have to add all the books together then arrange it

$6+3+2=11$

Thus the total arrangement are:

$11!$

$39,916,800$