To determine the number of combinations of three different flavours of ice cream you can select from 6 available flavours, you need to calculate the number of ways to choose 3 flavours from a set of 6, where the order in which the flavours are chosen does not matter. This is a combination problem.

The formula for combinations is:

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

Where:

• $n$ is the total number of items (flavours) available,
• $r$ is the number of items (flavours) you want to select.

In this case, $n = 6$ (the number of ice cream flavours), and $r = 3$ (the number of flavours you want to choose).

So, we can calculate:

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

Thus, there are 20 different combinations of 3 flavours that you can select from 6 flavours.

Let me know if you'd like more details or have any questions!

Additional Questions:

1. How would the number of combinations change if you had to select 4 flavours instead of 3?
2. How can the formula for combinations be applied in real-life situations other than choosing ice cream flavours?
3. What would the formula look like if you had to choose all 6 flavours?
4. How do combinations differ from permutations in terms of order?
5. How do you calculate combinations if repetitions are allowed?

Tip:

Remember that the order does not matter in combinations. If you were to arrange the flavours in a specific order, that would be a permutation, and the calculation would be different!