SOLUTION: A pizza shop advertises that they have 8 toppings, and they sell large, medium, and small pizzas. On a small pizza, you must choose 3 different toppings. On a medium pizza, you mus

Question 394731: A pizza shop advertises that they have 8 toppings, and they sell large, medium, and small pizzas. On a small pizza, you must choose 3 different toppings. On a medium pizza, you must choose 4 different toppings, and on a large, you must choose 5 different toppings. How many different pizzas can they make?
Choose the answer and explain the reason to choose your response
475
219
182
657
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
my mistake
I should have used combinations instead of permutations since order does not matter
small pizza: 8C3=336/6=56
medium pizza: 8C4=1680/24=70
large pizza: 8C5=6720/120=56
total pizzas= 56+70+56=182
==
ignore below
these answers do not make sense!
--
for the small pizza there are 8P3=8*7*6=336 different types of small pizzas
for the medium pizza there are 8P4=8*7*6*5=1680
for the large pizza there are 8P5=8*7*6*5*4=6720
so there should be 336+1680+6720=8736 different pizzas
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