You need to determine the number of possible combinations when you choose 4 appetizers out of 11 options in the dinner menu. Assuming that you are not going to repeat appetizers, to determine this number you have to apply combinations, using the formula:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
Where
n is the number of options available
r is the number of options you have to choose, with no repetition, and the order doesn't matter.
For this exercise:
n=11
r=4
The combination can be determined as follows:
[tex]\begin{gathered} C(11,4)=\frac{11!}{4!(11-4)!} \\ C(11,4)=\frac{11!}{4!\cdot7!} \\ C(11,4)=\frac{39916800}{24\cdot5040} \\ C(11,4)=330 \end{gathered}[/tex]
There are 330 combinations possible to choose 4 out of 11 appetizers from the menu.
