there are six different flavours of icecream. If you want to take three different scoops, how many variations can be there

You have six different flavors of ice cream and want to choose 3 different scoops. Since the order in which you choose the scoops doesn't matter, this is a combination problem.

The formula for combinations is:

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

where:
- \( n \) is the total number of items (6 flavors),
- \( r \) is the number of selections to be made (3 scoops).

Substituting the values into the formula:

\[
\binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6!}{3!3!}
\]

Simplifying:

\[
= \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = \frac{120}{6} = 20
\]

So, there are 20 different combinations of 3 scoops from 6 different flavors.

Would you like more details on combinations or have any other questions?

Here are 5 related questions:
1. How would the number of combinations change if you could repeat flavors?
2. What if you had to choose 2 scoops instead of 3?
3. How does the combination formula change for larger sets?
4. What if the scoops were selected in a specific order?
5. How does this compare to choosing 3 scoops from 7 flavors?

**Tip:** In combination problems, order does not matter; in permutation problems, order matters.

There are six different flavours of ice cream. If you want to take three different scoops, how many variations can be there?

Explore how to calculate the number of possible combinations when choosing 3 different scoops from 6 flavors of ice cream. Learn about the combination formula and its application in this step-by-step solution, ideal for students in Grades 9-12.

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