For the new fall season, a network president has 7 shows in development, and 5 openings in the prime time schedule. In how many ways can she arrange new shows to fit into the schedule?
There are ways to arrange new shows to fit into the schedule.

Step 1 ：We are given that a network president has 7 shows in development, and 5 openings in the prime time schedule. We are asked to find out in how many ways she can arrange new shows to fit into the schedule.

Step 2 ：This is a combination problem. We are choosing 5 shows out of 7, and the order in which we choose them does not matter.

Step 3 ：The formula for combinations is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 4 ：Substituting the given values into the formula, we get \(C(7, 5) = \frac{7!}{5!(7-5)!}\)

Step 5 ：Solving this, we get the number of combinations as 21.

Step 6 ：Final Answer: There are \(\boxed{21}\) ways to arrange new shows to fit into the schedule.