How many ways can 3 topping pizzas be made with the 10 toppings a pizzeria has? Assume no topping is used twice.

To determine how many ways 3-topping pizzas can be made from 10 available toppings, we can use the concept of combinations, since the order in which the toppings are chosen does not matter. The number of ways to choose \( r \) toppings from \( n \) available toppings is given by the combination formula: \[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \] In this case, we have \( n = 10 \) (the total number of toppings) and \( r = 3 \) (the number of toppings we want to choose). Plugging in these values, we get: \[ \binom{10}{3} = \frac{10!}{3!(10-3)!} = \frac{10!}{3! \cdot 7!} \] Now, we can simplify this expression: \[ \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} \] Calculating the numerator: \[ 10 \times 9 = 90 \] \[ 90 \times 8 = 720 \] Now calculating the denominator: \[ 3 \times 2 \times 1 = 6 \] Now we divide the numerator by the denominator: \[ \frac{720}{6} = 120 \] Thus, the number of ways to make a 3-topping pizza with 10 available toppings is \( \boxed{120} \).