How many 3 topping pizzas are possible if the pizza parlor has 9 different topping?

Answer 1

You pose an interesting question and its easy to solve once you realize it has to do with permutations and combinations. First, here's what you need to know: A combination is the arrangement of a distinct number of objects without regard to their order. You have a distinct number of toppings, 10. You want 4 toppings on each Pizza, and you don't care in what order they are put on the dough. So here is how to solve it: C(n, r), which equals n!/[(n - r) r!]. Now let's substitute the formula with the pizza information: C(10, 4) = 10!/[(10 - 4) 4!].

C(10, 4) = (10 x 9 x 8 x 7 x 6!)/6! 4!

The 6! in the numerator cancels with the 6! in the denominator

C(10, 4) = (10 x 9 x 8 x 7)/4!

C(10, 4) = 5040/4!

C(10, 4) = 5040/(4 x 3 x 2 x 1)

C(10, 4) = 5040/24

C(10, 4) = 210

So, that means if you were in a pizza parlor and they have 10 toppings to choose from, you can create 210 pizzas that each have 4 toppings. That's a lot of pizza, so be sure to grab some soda!

Answer 2

This is 8C3. There are 56 possible combinations of three toppings out of 8.

abc abd abe abf abg abh acd ace acf acg ach, ade adf adg adh, etc... This is the fourth entry in the 8 row of Pascal's triangle.