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?

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- May 27th 2009, 09:53 PMkrzyriceNeed 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?

- May 27th 2009, 11:09 PMRapha
Does this mean, there are 10 choices for meats + 10 choices for vegetables?

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?"

Then you have to multiply by 3

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