Paul was making a pizza. He had 12 different toppings from which to choose. How many different pizzas could he possibly make with 4 toppings?

Question

Im having a hard time with these problems

Answer 1

This is a basic combination problem.

You want the number of combinations of 12 items taken 4 at a time.

Remember the symbol for factorial is !

combinations of 12 items taken 4 at a time =  (12!) /((12 -4)! x 4!)

                                                              = 12!/(8! x 4!)

                                                              = (12 x 11 x 10 x 9) /( 4 x 3 x 2 x 1)

                                                              = 1180 / 24

                                                              = 495

 

Not that we use combinations rather than permutations because the order in which the toppings are chosen is unimportant; i.e.

1. mushrooms, peppers, onions, and bacon

is the same as

2. bacon, peppers, mushrooms, and onions