# Need help figuring out combinations

• May 27th 2009, 09:53 PM
krzyrice
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?
• May 27th 2009, 11:09 PM
Rapha
Quote:

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?

Quote:

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?"

Quote:

Originally Posted by krzyrice
If you can choose between a small, medium, or large sandwich

Then you have to multiply by 3

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