# Thread: Need help figuring out combinations

1. ## Need help figuring out combinations

At subway there are 10 choices for meats and vegetables on your sandwich. If you can choose between a small, medium, or large sandwich and want to mix 4 of the toppings, how many different sandwiches can you order?

2. Originally Posted by krzyrice
At subway there are 10 choices for meats and vegetables on your sandwich.
Does this mean, there are 10 choices for meats + 10 choices for vegetables?

Originally Posted by krzyrice
and want to mix 4 of the toppings, how many different sandwiches can you order?
Is it possible to take the same meat twice?

If not, the solution for this problem is $\displaystyle \begin{pmatrix}20 \\ 4 \end{pmatrix}$ or
$\displaystyle \begin{pmatrix}10 \\ 4 \end{pmatrix}$, depends on "are there 10 meats and 10 vegetables each?"

Originally Posted by krzyrice
If you can choose between a small, medium, or large sandwich
Then you have to multiply by 3

$\displaystyle 3*\begin{pmatrix}20 \\ 4 \end{pmatrix}$