A certain ice cream parlor offers six flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors. the number of ways to choose a cone if order doesnt matter is

To find the number of ways to choose an ice cream cone with three scoops of ice cream, all different flavors, from six available flavors, where order doesn't matter, you can use combinations. The formula for combinations is:

\[
\binom{n}{r} = \frac{n!}{r!(n - r)!}
\]

where:
- \( n \) is the total number of items (in this case, flavors),
- \( r \) is the number of items to choose (in this case, scoops of ice cream),
- \( ! \) represents the factorial of a number.

Here, \( n = 6 \) and \( r = 3 \).

\[
\binom{6}{3} = \frac{6!}{3!(6 - 3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = \frac{120}{6} = 20
\]

Thus, there are 20 ways to choose 3 different flavors from 6, where the order does not matter.

Would you like a detailed explanation or have any questions?

Here are 5 related questions:
1. How would the calculation change if two flavors could be the same?
2. How many ways can you choose three flavors if the order **does** matter?
3. If the parlor introduces two more flavors, how many ways can you choose 3 different flavors?
4. How many ways can you choose 4 different flavors from the same 6 flavors?
5. How many combinations are possible if you are allowed to pick only 2 flavors?

**Tip:** When order doesn't matter, use combinations; when order matters, use permutations!

A certain ice cream parlor offers six flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors. The number of ways to choose a cone if order doesn't matter is:

Learn how to calculate the number of ways to choose 3 different flavors of ice cream from 6 available options, using combinations. The problem uses the combination formula C(n, r) to find there are 20 possible ways. Suitable for students in Grades 9-11.

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