Question

A set of 24 different books consists of 12 maths books and 12 physics books. How many ways
are there to:

(b) arrange the entire set on a given shelf so that the maths books are all adjacent?

MY THOUGHT: I am thinking...there are 12! ways to arrange the books into one block, just one book. It's more like we have 13 books now, and there are 13! ways to arrange them, so 12!*13!...I dont know whether I need to multiply by 12! the number of ways to arrange the physics books.

Answer 1

Your reasong looks good. The answer is indeed 13!*12!

Answer 2

Thank you. I was confused about the fact that we may have to write the number of ways to arrange the other books.

Answer 3

Godd work!

Answer 4

thank you guys!

Answer 5

There is one good way to approach problems like these

Answer 6

please tell me @ganeshie8

Answer 7

You want all the 12 math books together. So put all the math books in a bag and tie them.

Answer 8

After that, you will see below :
1) 12 physics books
2) one bag of math books

Total 13 objects, yes ?

Answer 9

yes!

Answer 10

How many ways can you arrange 13 objects ?

Answer 11

13!

Answer 12

Yes, next open the bag with 12 math books.

You can further arrange the books inside this bag in 12! ways, yes ?

Answer 13

yes!

Answer 14

13! ways for total objects
12! ways for the items inside bag

together we get 13!*12! total ways

Answer 15

Great!

Answer 16

i really appreciate this