How many different types of pizza with two toppings can we order, if we have 8 choices of size, 8choices of thickness, and 6 choices of toppings.
Question
How many different types of pizza with two toppings can we order, if we have 8 choices of size, 8 choices of thickness, and 6 choices of toppings?
Solution
To solve this problem, we need to consider each choice separately and then combine them.
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Size: We have 8 choices of size.
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Thickness: We have 8 choices of thickness.
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Toppings: We have 6 choices of toppings, but we want to choose 2. This is a combination problem, because the order in which we choose the toppings does not matter. The number of ways to choose 2 toppings from 6 is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of options, k is the number of options to choose, and "!" denotes factorial.
So, C(6, 2) = 6! / [2!(6-2)!] = (65432) / (21432) = 15.
So, the total number of different types of pizza we can order is the product of the number of choices for each characteristic: 8 (size) * 8 (thickness) * 15 (toppings) = 960.
Therefore, we can order 960 different types of pizza with two toppings given 8 choices of size, 8 choices of thickness, and 6 choices of toppings.
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