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A pizza shop has 12 toppings from which to choose. If 3 toppings are chosen randomly for a pizza, what is the probability that it is topped with pepperoni, onion, and sausage?

$\frac{1}{220}$

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Missouri State University

McMaster University

Harvey Mudd College

Numerade Educator

All right, so we have 12 toppings. We want three. Um, it doesn't matter what order would choose them in. So this is a combination of 12. Choose three, which means that we have 12 Tom's, 11 times 10 and then we're gonna divide that by three times, two times one, because the order doesn't matter. So 12 times, 11 times tiene is 1320 three times, two times once six. So we divide 13 20 by six. We have 220 possible three topping combinations. Now who in those exact three. Then we want to do a permutation, then of three items. But we want to choose all three of them. So this is three times two times one. So there are six ways that I could get Pepperoni, onion and sausage. So for probabilities, say, those are the six possible options I want out of the total three toppings. So we divide six by 220 we get 0.27 which is about 2.7% chance that that is the toppings that I end up with. If I have 12 and I have to choose three