You decide to order a large two topping pizza. The pizza place has 10 toppings to choose from. You like to live on the edge, so you tell the person taking your order to surprise you with the two toppings. If the pizza maker picks the two toppings at random, what is the probability that you end up with pepperoni and sausage?

Question

anonymous · Answer

There are two ways to get pepperoni and sausage - P&S or S&P.

There are $\dbinom{10}2$ ways to order toppings.

The probability is then
$$\dfrac{2}{\dbinom{10}2}=\frac{2}{45}$$