Answer :
Combinations without repetition are used to calculate the number of ways to choose 5 different ice cream flavors from 30, which is '30 choose 5'. For toppings, '7 choose 2' is used, and these combinations are multiplied together for the total number of ways to select ice cream and toppings.
To answer question (a), which asks how many ways you can select a bowl of 5 scoops of ice cream if each scoop is a different flavor out of 30 flavors, you would use combinations without repetition.
The formula for this is given by the equation N choose r, where N is the total number of options and r is the number of selections made. In this case, it would be 30 choose 5 which is calculated as 30! / (5! * (30-5)!).
For question (b), which asks how many ways can you select 5 scoops of ice cream and 2 toppings from a set of 7 toppings, you would calculate the combinations for the ice cream as in part (a) and then multiply by the combinations of 2 toppings from 7, which is 7 choose 2. Therefore, the total combinations would be 30 choose 5 multiplied by 7 choose 2.
