The answer explains how to calculate combinations with and without repetition, as well as using the Multiplication Principle for multiple selections.
Combinations with repetition: If we can include repetitions, the number of ways to choose 3 toppings from 10 is calculated using combinations with repetition formula. Since you can have more than one scoop of a particular topping, the formula used is (n + r - 1) choose r, where n is the number of toppings and r is the number of choices. In this case, it would be (10 + 3 - 1) choose 3.
Combinations without repetition: When choosing 3 scoops of different ice cream flavors from 5 options, the number of different combinations without repetition is determined using the combination formula. You would calculate 5 choose 3, which represents selecting 3 different flavors from 5.
Multiplication Principle: When selecting from multiple sets without repetition, the total number of sequences is found by multiplying the number of choices in each set. For example, if you have 40 options on day one, 39 on day two, and 38 on day three, the total sequences would be 40 39 38.
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