Question

If no two books are alike, in how many ways $2$ red, $3$ green, and $4$ blue books be arranged on a shelf so that all the books of the same color are together ?

Answer 1

$\Rightarrow$ In each arrangement red colour books can be arranged in $2!ways$

$\Rightarrow$ green colour books in $3!ways$

and blue colour books in $4!ways$

Total 3 units are arranged in $3!=6ways$

$\therefore$ Total no. of ways $=3!\times 2!\times 3!\times 4!$

$=6\times 2\times 6\times 24$

$=1728$