MHT CET · Maths · Permutation Combination
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
- A 576
- B 288
- C 3456
- D 1152
Answer & Solution
Correct Answer
(C) 3456
Step-by-step Solution
Detailed explanation
There are 3 books on physics, 2 books on Chemistry and 4 books on Mathematics.
All Physics books and Mathematics books are kept together.
\(\therefore\) All Physics books will be considered as 1 unit and all Mathematics books are also considered as 1 unit.
\(\therefore\) 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
\(\begin{aligned}
\therefore \text {Total number of arrangements } & =4!\times 3!\times 4! \\
& =3456
\end{aligned}\)
All Physics books and Mathematics books are kept together.
\(\therefore\) All Physics books will be considered as 1 unit and all Mathematics books are also considered as 1 unit.
\(\therefore\) 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
\(\begin{aligned}
\therefore \text {Total number of arrangements } & =4!\times 3!\times 4! \\
& =3456
\end{aligned}\)
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