Exercise 1. Aline's class contains thirty students, all of different heights. For the class photo, to ensure everyone is clearly visible, the ten shortest students in the class must be placed in the front row and the ten tallest students must be placed in the back row (the remaining ten students are therefore in the middle). How many ways are there to distribute the students across the thirty available spots while respecting these conditions?
Solution to Exercise 1 First, we need to distribute the ten smallest students in the first row. There are $10 \times 9 \times 8 \times \ldots 2 \times 1=10$! ways to do this (there are 10 places for the first student, then 9 places for the next, etc...). Similarly, there are 10! ways to place the 10 tallest students in the last row, and 10! ways to place the remaining 10 students in the middle row. Since these distributions are independent, there are therefore $(10!)^{3}$ ways to distribute the students as desired.

Graders' Comment: Almost all students scored 7 points. There was only one rare slip-up: multiplying 10! by 3 instead of raising it to the power of 3.