ANSWERS: 6
  • 21; 7times 3 equals 21
  • To find this, we need to find the number of possible combos for each kind of pizza. In this example, each number is a non-specific topping. Note that no pizza can have the same topping twice. I'm sure there is an easier way to do this, but I can't think of it right now. Zero topping pizzas (1): One topping pizzas (7): 1 2 3 4 5 6 7 Two topping pizzas (21): 12 13 14 15 16 17 23 24 25 26 27 34 35 36 37 45 46 47 56 57 67 3 topping pizzas (35): 123 124 125 126 127 134 135 136 137 145 146 147 156 157 167 234 235 236 237 245 246 247 256 257 267 345 346 347 356 357 367 456 457 467 567 Logically there can only be as many 4 topping combinations as there are 3 topping combos, because each 4 topping pizza is actually an absence of 3 toppings. (35) Same for the number of 5 toppings as 2 topping pizzas (21) Ditto 6 and 1, 7 and zero. So to find the total number of combos, we add the number of zero, one, two, three, four, five, six and seven topping combinations, then multiply that number by the number of potential crusts, since each pizza must have exactly one crust. So we get: 3(1+7+21+35+35+21+7+1) or: 384
  • 3 times 7!(7 time 6 times 5 ...)
  • A pizza can have only one type of crust at a time. But it can have any number of toppings up to 7. 3 types of pizza with no toppings. double that and put anchovies on half of them. That's six kinds. double that and put pepperoni on half of them. That's 12 kinds. double that and put sausage on half of them. That's 24 kinds. double that and put chicken on half of them. That's 48 kinds. double that and put olives on half of them. That's 96 kinds. double that and put peppers on half of them. That's 192 kinds. double that and put capers on half of them. That's 384 kinds for seven different types of topping.
  • 3 x 2^7 = 384

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