Question

In a library, there are m books of mathematics and n books of natural science. They can be placed on a shelf in $1209600$ ways so that the books of the same subject are not separated.If $m\ge n$. then m $=$

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is B $7$

Mathematics books and natural science books could permute in m! and n! way and we could arrange them in 2!
$m!\times n!\times 2!$ $=$ 1209600

By trial and error,
$m!\times n!$ $=$ $7!\times 5!$