At the movie, Shana wants to get snacks for her friends. How many ways can she select two types of candy and four types of soda from the six types of candy and eight types of soda available?

To determine how many ways Shana can select two types of candy and four types of soda from the available options, we'll break the problem into two parts and then multiply the results.

1. **Selecting Two Types of Candy:**
   Shana has 6 types of candy to choose from, and she needs to select 2. The number of ways to choose 2 types of candy from 6 is given by the combination formula:

   \[
   \text{Number of ways to choose 2 types of candy} = \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15
   \]

2. **Selecting Four Types of Soda:**
   Shana has 8 types of soda to choose from, and she needs to select 4. The number of ways to choose 4 types of soda from 8 is also given by the combination formula:

   \[
   \text{Number of ways to choose 4 types of soda} = \binom{8}{4} = \frac{8!}{4!(8-4)!} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70
   \]

3. **Total Number of Ways:**
   Since the candy and soda choices are independent of each other, we multiply the number of ways to choose the candy by the number of ways to choose the soda:

   \[
   \text{Total number of ways} = 15 \times 70 = 1050
   \]

Therefore, Shana can select two types of candy and four types of soda in **1,050** different ways.

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:

1. What if Shana wanted to select three types of candy instead of two?
2. How many ways can she select one type of candy and two types of soda?
3. What is the probability that Shana selects a specific candy and a specific soda combination?
4. How many ways can Shana select five types of soda from eight options?
5. What if Shana could only choose one type of candy and one type of soda? How many ways would that be?

**Tip:** When dealing with combinations, remember that order doesn't matter. Use the combination formula \(\binom{n}{k}\) to calculate how many ways you can choose \(k\) items from \(n\) items.

Discover how to calculate the number of ways Shana can select 2 types of candy from 6 options and 4 types of soda from 8 options using combinatorics. This step-by-step guide covers the combination formula and key counting principles. Ideal for students in Grades 8-10.

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