Please show all your work out

Question

There are 5 mathematics,4physics and 5 chemistry books. In how many ways can you arrange 4 mathematics, 3 physics and 4 chemistry books:

{i}: If the books on the same subjects are arranged together, but the order in which the books are arranged within a subject doesnt matter.

{ii}:If books on the same subjects are arranged together and the order in which books are arranged within subject matters.

Answer 1

You can select the books to be arranged in 5*4*5 = 100 ways. And you can arrange the sets selected on the shelf in 6 ways.

 

If the order does matter, that is the order is specified ahead of time, there is only 1 way to do that; therefore, the 600 ways above is all the possible arrangements.

 

But if each set is to be arranged within itself then you need to multiply the 600 by 5!*4!*5! which is a big number which I'll leave for you to calculate.