An Italian restaurant serves pasta dishes with the following options:

Pasta - angel hair, manicotti, or linguine
Sauce - tomato, alfredo, garlic, or meat
Cheese - parmesan or cheddar

How many different pasta dishes are possible, assuming one item is chosen from each category?
I'm so stuck on this question and I don't have any idea on how to solve it...any help?

Take the options and write them all down: ie. angel hair, tomato,parmesan;

angel hair alfredo, parmesan, angelhair, garlic, parmesan, angel hair meat, parmesan....etc.

Then count them. This is the hard way.

you can pick the pasta in 3 ways,

for each of those you can pick the sauce in 4 ways,
and for each of those 12 ways so far, you can pick the cheese in 2 ways.

so there are 24 different pasta dishes possible,
note that 24 = 3x4x2

...Looks and seems hard...but I'll try. Thanks!

-MC

Reiny, I just saw your answer...Thanks!

-MC

The answer choices are:

a.24
b.9
c.32
d.18
-MC

I think it might be A

To solve this question, you need to determine the number of possible combinations for each category (pasta, sauce, and cheese) and then multiply them together to find the total number of dishes.

Let's start by counting the number of choices for each category:

1. Pasta: There are 3 options (angel hair, manicotti, and linguine).
2. Sauce: There are 4 options (tomato, alfredo, garlic, and meat).
3. Cheese: There are 2 options (parmesan and cheddar).

To find the total number of possible combinations, you multiply the number of options for each category:

3 (pasta options) x 4 (sauce options) x 2 (cheese options) = 24

Therefore, there are 24 different pasta dishes possible.

Alternatively, you can also calculate it by listing out all the possible combinations:
- Angel hair pasta with tomato sauce and parmesan cheese
- Angel hair pasta with tomato sauce and cheddar cheese
- Angel hair pasta with alfredo sauce and parmesan cheese
- Angel hair pasta with alfredo sauce and cheddar cheese
- Angel hair pasta with garlic sauce and parmesan cheese
- Angel hair pasta with garlic sauce and cheddar cheese
- Angel hair pasta with meat sauce and parmesan cheese
- Angel hair pasta with meat sauce and cheddar cheese
- Manicotti pasta with tomato sauce and parmesan cheese
- Manicotti pasta with tomato sauce and cheddar cheese
- Manicotti pasta with alfredo sauce and parmesan cheese
- Manicotti pasta with alfredo sauce and cheddar cheese
- Manicotti pasta with garlic sauce and parmesan cheese
- Manicotti pasta with garlic sauce and cheddar cheese
- Manicotti pasta with meat sauce and parmesan cheese
- Manicotti pasta with meat sauce and cheddar cheese
- Linguine pasta with tomato sauce and parmesan cheese
- Linguine pasta with tomato sauce and cheddar cheese
- Linguine pasta with alfredo sauce and parmesan cheese
- Linguine pasta with alfredo sauce and cheddar cheese
- Linguine pasta with garlic sauce and parmesan cheese
- Linguine pasta with garlic sauce and cheddar cheese
- Linguine pasta with meat sauce and parmesan cheese
- Linguine pasta with meat sauce and cheddar cheese

Counting all these combinations, you will find that there are 24 different pasta dishes possible.