A shelf has $10$ distinct books of which $3$ are Math,$ 4$ are English and $3 $ are Science books. In how many ways can you arrange these books such that all English books will be placed in the center?
I have tried to answer the arrangement where each kind of books will be together-> $(3!.4!.3!.3!=5,184)$ but this time I can not determine which factorial to include.
Best Answer
In total, there are $10!$ ways to arrange 10 books. But lets fix 4 English books in the centre. Now there are $6!$ ways to arrange the remaining items. How many ways can we arrange the 4 English books in the centre? That would be $4!$. So the answer would be $4!*6! = 17280.$