Generalised permutation combinations

Question

In how many ways can a dozen books be placed on four distinguishable shelves

if no two books are the same, and the positions of the books on the shelves matter?

(Hint: Break this into 12 tasks, placing each book separately. Start with the sequence 1,2,3,4 to

represent the shelves. Represent the books by bi, i = 1, 2, ..., 12. Place b1 to the right of one of

the terms in 1, 2, 3, 4. Then successively place b2, b3, ..., and b12.)

Comments

its case of different objects (label)distribute in different(label) box ... so here box and books both position matter ..

 

12! 4! $\div 3! 3! 3! 3! 4!$ + 12! 4!$\setminus 4! 3! 3! 2! 2!$ + ... like was many cases

Answer 1

You can visit the link mentioned below for further reading. The explanation is a good one. :) 

https://math.stackexchange.com/questions/1246694/how-many-ways-can-n-books-be-placed-on-k-distinguishable-shelves-if-no-2-books-a