Step 2 of 2: How many different combinations of 3
 movies can she rent if she wants at least one comedy?


To solve this problem, we need to calculate the number of ways to rent 3 movies from a given selection while ensuring at least one of them is a comedy.

We’ll break it down step by step:

### 1. Total combinations of 3 movies:
Let’s assume there are \( N \) total movies available for rent (including both comedies and non-comedies).

The number of ways to choose 3 movies from \( N \) total movies (without any restriction) is given by the combination formula:
\[
\text{Total combinations} = \binom{N}{3} = \frac{N!}{3!(N-3)!}
\]

### 2. Combinations with no comedies:
Let \( C \) be the number of comedies available. The number of ways to choose 3 movies where none are comedies would depend on the number of non-comedies, say \( N - C \). The number of ways to choose 3 non-comedies is:
\[
\text{Non-comedy combinations} = \binom{N - C}{3}
\]

### 3. Combinations with at least one comedy:
The number of ways to choose 3 movies with at least one comedy is the total number of combinations minus the number of combinations with no comedies:
\[
\text{Combinations with at least one comedy} = \binom{N}{3} - \binom{N - C}{3}
\]

If you provide the total number of movies (\( N \)) and the number of comedies (\( C \)), I can calculate the exact result for you!

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Would you like to proceed with specific values, or have any further clarifications?

### Related Questions:
1. What is the probability of selecting only comedies?
2. How many ways can she select exactly 2 comedies?
3. What happens if she rents only non-comedies?
4. How would the combination change if she rents 4 movies?
5. Can we extend this problem to selecting movies over multiple days?

**Tip:** Always check the conditions (like "at least one comedy") carefully when solving combination problems.

Step 2 of 2: How many different combinations of 3 movies can she rent if she wants at least one comedy?

Learn how to calculate the number of ways to rent 3 movies, ensuring at least one is a comedy. This problem explores key combinatorial concepts, including the formula for combinations and the subtraction method. Suitable for students in Grades 9-12.

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