Question

Judy has three sets of classics in literature, each set having four volumes. In how many ways can she put them in a bookshelf so that books of each set are not separated?

Answer 1

Books of each set are together, Three sets can be placed in 3! ways
Each set has 4 volumes, these 4 volumes can be placed in 4! ways.
But we have two more sets with 4 volumes so total no. of arrangements of books of each set = 4!+4!+4!=3*4!
so total no. of ways
3! *3* 4!

Answer 2

but that's not right....

Answer 3

do you have the answer?

Answer 4

yes. 82,944

Answer 5

btw..i also don't know where 3! came from in your solution

Answer 6

We have three different sets, we can arrange 3 sets in 3! ways.
For one such arrangement, no. of arrangements of books=\(3\times 4!\)
see the attached file

Answer 7

..so how do you get 82,944 from that?

Answer 8

I get it, the individual arrangements of books is
\[4!*4!*4!\]
it won't sum but multiplied
so total no. of ways= 3!*4!*4!*4!

Answer 9

checked it now, it's 82944

Answer 10

@lgbasallote sorry for the mistake, do you understand this?

Answer 11

i see...but how did you get those numbers?

Answer 12

which no.s ?

Answer 13

why 3!*4!*4!*4!

Answer 14

let me be more specific...

first... why 4!

Answer 15

I have 4 books, 4 books can be arranged in 4! ways
since we have three sets of 4 books, these three sets can be arranged in
4!*4!*4!

Answer 16

wait wait..go slow

Answer 17

Ok, I'll be steady

Answer 18

4 books can be arranged in 4! ways...is this for 4 slots?

Answer 19

yeah

Answer 20

hmm...then why 4!4!4!

Answer 21

now, If I had 12 books, I could arrange them in 12! ways, couldn't I?

Answer 22

@lgbasallote ???

Answer 23

yes

Answer 24

But we have a constraint here, we can't mix the books, books of each set should not be separated