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1. \({11 \choose 3} = 165\) choices, since you have to select a 3-element subset of the set of 11 toppings.

2. \({10 \choose 3} = 120\) choices, since you must select 3 of the 10 non-pineapple toppings.

3. \({10 \choose 2} = 45\) choices, since you must select 2 of the remaining 10 non-pineapple toppings to have in addition to the pineapple.

4. \(165 = 120 + 45\) choices, which makes sense because every 3-topping pizza either has pineapple or does not have pineapple as a topping.