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I have another question on my stats homework, relating to degrees of freedom. However, I have NO idea how this question even relates to degrees of freedom! I understand degrees of freedom on their own, i.e. how when calculating standard deviation you divide by df instead of total n because the centered scores always equal out to zero, but I don't get how that relates to this question. Is the professor just trying to throw us off with irrelevant info? Is the answer simply 10?

Last Saturday, Karl went to a party at a friend’s house. His friend had ordered 4 medium (8 slice) pizzas from Flying Tomato Pizza. There was a “Veggie” pizza (with Mushroom, Green Pepper, Tomato, & Onion), a “Greek” pizza (with Black Olives, Tomato, Onion, & Feta Cheese), and two “Meat Lovers” pizzas (with Pepperoni, Ham, Bacon, & Italian Sausage).

Karl is vegetarian, and when he goes to get a slice of pizza, there remain 6 slices of the “Veggie” pizza, 4 slices of the “Greek” pizza, and 9 slices of the “Meat Lovers” pizzas. How many degrees of freedom does Karl have in picking his slice of pizza?

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My guess is one, because he can choose between veggie or greek pizza. I.e, the number of degrees of freedom are the number of different "types of things" he can choose. So his single degree of freedom is $\text{kind of pizza}$. If he could pick multiple slices, then he might have two: $\text{kind of pizza}$ and $\text{number of slices}$. Seems like a forced example though.

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