Question 222376
Since order doesn't matter, we're going to use the combination formula


*[Tex \LARGE \textrm{_{n}C_{r}=\frac{n!}{(n-r)!r!}}]


*[Tex \LARGE \textrm{_{8}C_{3}=\frac{8!}{(8-3)!3!}}] Plug in n=8 and r=3


*[Tex \LARGE \textrm{_{8}C_{3}=\frac{8!}{5!3!}}] Subtract 8-3 to get 5


*[Tex \LARGE \textrm{_{8}C_{3}=\frac{40320}{5!3!}}] Calculate 8! to get 40,320 (note: if you need help with factorials, check out this solver)


*[Tex \LARGE \textrm{_{8}C_{3}=\frac{40320}{(120)(3!)}}] Calculate 5! to get 120


*[Tex \LARGE \textrm{_{8}C_{3}=\frac{40320}{(120)(6)}}] Calculate 3! to get 6



*[Tex \LARGE \textrm{_{8}C_{3}=\frac{40320}{720}}] Multiply the values 120 and 6 to get 720


*[Tex \LARGE \textrm{_{8}C_{3}=56] Divide 40,320 by 720 to get 56



So 8 choose 3 (where order does not matter) yields 56 unique combinations. So there are 56 different ways to make three-topping pizzas.