The studio owner wants each child to have a fair chance of being placed in either class, so she must not do the following:
Option C is the answer.
Using a random number generator, assign each child a number, eliminating any duplicate numbers. After each child is assigned a number, list the assigned numbers in ascending order. Assign the children with the first 20 numbers on the ascending list to Class Alpha, and assign the children with the last 20 numbers on the ascending list to Class Beta.