Final answer:
There are 1800 different ways to choose 3 kinds of ice cream and 2 toppings from 10 kinds of ice cream and 6 kinds of toppings, calculated using combinations formula for independent events.
Step-by-step explanation:
The question involves finding the number of ways to choose 3 kinds of ice cream and 2 toppings from a given selection. To solve this, we use combinatorics, a branch of mathematics that deals with counting combinations and permutations of sets of elements.
To find the number of ways to choose 3 kinds of ice cream from 10 available options, we calculate the combinations using the combination formula which is C(n, k) = n! / (k!(n-k)!) where 'n' is the total number of options and 'k' is the number of selections to be made. For ice cream, this is C(10, 3).
Similarly, to find the number of ways to choose 2 toppings from 6 options, we use the formula C(6, 2).
The total number of ways to choose the ice cream and toppings together is the product of these two combinations as independent events. Thus, the calculation is C(10, 3) × C(6, 2).
Calculating the combinations, we get:
- C(10, 3) = 10! / (3!(10-3)!) = 120
- C(6, 2) = 6! / (2!(6-2)!) = 15
Therefore,
120 (from ice cream) × 15 (from toppings) = 1800
So, there are 1800 different ways to choose 3 kinds of ice cream and 2 toppings from the dessert buffet.