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

the number of ways to order 3 topping from a set of 13 is \[\binom{13}{3}\] read "thirteen choose three" sometimes written as \(_{13}C_3\) or even \(^{13}C_3\) and computed via \[\binom{13}{3}=\frac{13\times 12\times 11}{3\times 2}\]
that is your denominator

Answer 2

your numerator is the number of ways to choose 3 out of 8, i.e. \[\binom{8}{3}\]