Longhorn Pizza has the following number of topping options available: four vegetables, two meats, and two cheeses. A pizza is ordered with exactly four toppings. What is the probability that the pizza is ordered with exactly two vegetables, one meat, and one cheese? Use complete sentences to explain the probability. In your final answer, include all of your calculations.

QUESTION POSTED AT 01/06/2020 - 04:22 PM

Answered by admin AT 01/06/2020 - 04:22 PM

This problem could be solved through using the combination in your scientific calculator. First, the probability must be presented in a fraction, wherein the numerator is the number of possibilities for a given condition and the denominator is the number of all possibilities. 

For the numerator, using the counting principle:

2 out of 4 vegetables* 1 out of 2 meats * 1 out of 2 cheese
4C2 * 2C1 * 2C1 = 24

For the denominator, 

4 toppings out of 8 available toppings = 8C4 = 70
The 8 toppings consist of 4 vegetables + 2 meat + 2 cheese

Thus, the probability would be 24/70 or 12/35. 
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