How many different pizzas can be ordered if a pizza can be selected with any combination of the following ingredients: anchovies, ham, mushrooms, olives, onion, pepperoni, and sausage?
Can someone give me a hint to this question.
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If you only take one topping, how many choices do you have? If you take only two toppings, how many choices do you have? All the way up to if you take all 7 toppings, how many ways can that be chosen? OK that one I'll do for you: 1. Then add up all your answers – imranfat Feb 13 '14 at 16:54
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Hint: a pizza corresponds to a set of ingredients. How many sets that are subsets of $\{1,2,...,7\}$ exist ? (each number represents an ingredient).
If you don't know how to compute this, here is a hint: For each ingredient you have two choices: put it or not put it (that is the question). So your total number of choices is the combination of all these individual choices.
Don't forget the special case of $\emptyset$ which is counted here, so if you consider that "no topping" is not a valid pizza then you should substract one to the formula.
Denis
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@imranfat Yes of course: Pizza Margherita (it appears that the toppings tomato, cheese and opregano are considered trivial by the problem statement) – Hagen von Eitzen Feb 13 '14 at 17:01
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This answer (contrary to the comment of your question by imranfat) does not distinguish the cases by number of topping, and allows you to get to the final formula directly. – Denis Feb 13 '14 at 17:13