Question

You and two friends visit a pizza shop. There are 13 toppings. 8 toppings are meat and the rest are vegetable. Each of you orders a different topping (no repeats) at random. What is the probability that your group orders only meat toppings?

Answer 1

This can be solved by treating the question as sampling without replacement.
\[P(3\ different\ meat\ toppings)=\frac{\left(\begin{matrix}8 \\ 3\end{matrix}\right)}{\left(\begin{matrix}13 \\ 3\end{matrix}\right)}=\frac{8\times7\times6}{13\times12\times11}\]