Final answer:
To find the number of different ways to make a sandwich from 5 meats, 6 veggies, and 3 cheeses, multiply the combinations of each: 10 ways to choose meats, 6 for veggies, and 3 for cheeses. The total is 180 different ways, which is option A.
Step-by-step explanation:
To determine the number of different ways to select 2 meats, 1 veggie, and 1 cheese for a sandwich when you are given 5 meats, 6 veggies, and 3 cheeses, we can use the principles of combinatorics. For meats, since the order doesn't matter, we will use combinations rather than permutations. For veggies and cheese, since we are only choosing one, it's a simple selection.
First, we select the 2 meats out of 5. This can be done in 5 choose 2 ways, which is calculated as 5! / (2! * (5-2)!) = 10 ways.
Next, we select 1 veggie out of 6, which can be done in 6 choose 1 ways, simply 6 ways.
Lastly, we select 1 cheese out of 3, which can be done in 3 choose 1 ways, simply 3 ways.
To find the total number of different ways to make the sandwich, we multiply the number of ways to choose each component: 10 (meats) * 6 (veggies) * 3 (cheeses) = 180 ways.
Therefore, the answer is A) 180 ways.