To determine how many different ways you can select 2 different flavors of ice cream for a sundae when there are 16 flavors available, you use combinations. Combinations are used when the order of selection does not matter.

The formula for combinations is:

$C(n, r) = \frac{n!}{r!(n-r)!}$

Where:

• $n$ is the total number of items to choose from (16 flavors),
• $r$ is the number of items to choose (2 flavors),
• $!$ denotes factorial, the product of all positive integers up to that number.

Substituting the values:

$C(16, 2) = \frac{16!}{2!(16-2)!} = \frac{16 \times 15}{2 \times 1} = 120$

Final Answer:

There are 120 different ways to select 2 different flavors of ice cream for a sundae.

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Would you like further clarification or an explanation of factorials? 😊

Here are 5 related questions for practice:

1. How many ways can you select 3 flavors from 16 flavors?
2. What if the order of the flavors mattered—how many ways can you select 2 flavors then?
3. How many ways can you select 2 flavors if there were 20 flavors instead of 16?
4. If you want 2 scoops of the same flavor, how many options do you have?
5. What if one of the flavors is unavailable—how does that change the number of ways?

Tip: Use combinations when order doesn’t matter and permutations when it does!