Kevin goes to the grocery store with his mom. As a treat, he is allowed to pick 3 kinds of candy from a selection of 6 or 2 kinds of ice cream from a selection of 4. How many different combinations of treats are possible?

This problem involves calculating the number of possible combinations for Kevin's treats, which consist of either candies or ice creams.

### Step 1: Calculate the number of candy combinations.
Kevin is allowed to pick 3 kinds of candy from a selection of 6. This is a combination problem, which can be solved using the formula for combinations:

\[
\text{Combination formula: } C(n, k) = \frac{n!}{k!(n-k)!}
\]

where:
- \( n \) is the total number of items to choose from,
- \( k \) is the number of items to choose.

Here, \( n = 6 \) (total kinds of candy) and \( k = 3 \) (number of kinds of candy he can choose).

\[
C(6, 3) = \frac{6!}{3!(6-3)!} = \frac{6!}{3!3!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20
\]

So, Kevin has 20 possible combinations of candies.

### Step 2: Calculate the number of ice cream combinations.
Kevin is allowed to pick 2 kinds of ice cream from a selection of 4. Again, we use the combination formula:

Here, \( n = 4 \) (total kinds of ice cream) and \( k = 2 \) (number of kinds of ice cream he can choose).

\[
C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{4!}{2!2!} = \frac{4 \times 3}{2 \times 1} = 6
\]

So, Kevin has 6 possible combinations of ice creams.

### Step 3: Add the combinations.
Since Kevin can either pick 3 kinds of candy or 2 kinds of ice cream, the total number of combinations is the sum of the two:

\[
\text{Total combinations} = 20 \, (\text{candy combinations}) + 6 \, (\text{ice cream combinations}) = 26
\]

Thus, Kevin has **26 different combinations** of treats.

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Do you need further details on this or any related questions?

Here are 5 related questions to expand your understanding:

1. How would the total change if Kevin could pick 2 kinds of candy instead of 3?
2. What if Kevin could choose both candy and ice cream? How would that affect the total combinations?
3. How would the formula change if Kevin were allowed to pick the same treat more than once?
4. Can you explain why we use combinations and not permutations in this scenario?
5. What if the store added 2 more kinds of candy to the selection? How would the result change?

**Tip:** When calculating combinations, remember that the order in which the items are chosen does not matter—this is the key difference from permutations.

Explore how to calculate the number of combinations for Kevin's treats. Learn to apply the combination formula to find how many ways Kevin can choose 3 kinds of candy from 6 or 2 kinds of ice cream from 4. Suitable for students in Grades 6-8.

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