There are $18$ students and $2$ rows of $11$ seats. How many ways can you arrange the students if the first row must be always full and the $7$ students left must sit together?
My solution = $18C11 \cdot 11! \cdot 7! \cdot 5$
$18C11$ to choose $11$ people to sit at the first row, $11!$ to arrange them, $7!$ to arrange the $2$nd row, $5$ because there are $5$ ways to arrange them while sitting together, but I was told it was wrong.
What is the correct answer?