If 3 books on Physics, 2 books on Chemistry and 4 books on Mathematics are to be arranged on a shelf so that…
If 3 books on Physics, 2 books on Chemistry and 4 books on Mathematics are to be arranged on a shelf so that all the Physics books are together and all the Mathematics books are together, then the number of such arrangements is
576
288
3456
1152
Solution
There are 3 books on physics, 2 books on Chemistry and 4 books on Mathematics.
All Physics books and Mathematics books are kept together.
$\therefore \quad$ All Physics books will be considered as 1 unit and all Mathematics books are also considered as 1 unit.
$\therefore \quad$ Physics, Mathematics and 2 Chemistry books can be arranged in 4 ! ways.
Also, 3 Physics and 4 Mathematics books can be arranged themselves in $3!\times 4$ ! ways
$\begin{aligned}
\therefore \quad \text { Total number of arrangements } & =4!\times 3!\times 4! \\
& =3456
\end{aligned}$