7. Distribute 16 identical books to 4 students, with each student getting at least one book and the number of books each student receives being different. The number of different distribution methods is $\qquad$ . (Answer with a number)
Answer 216.
Analysis Because decomposing 16 into the sum of 4 distinct positive integers has 9 different ways:
$$
\begin{array}{cllll}
16=1+2+3+10, & 16=1+2+4+9, & 16=1+2+5+8, & 16=1+2+6+7, & 16=1+3+4+8 \\
16=1+3+5+7, & 16=1+4+5+6, & 16=2+3+4+7, & 16=2+3+5+6, &
\end{array}
$$

Therefore, the number of different allocation methods that meet the conditions is $9 A_{4}^{4}=216$.