Question

a local pizzeria offers 11 topping for their pizzas and you can choose any 5 of them for one fixed price how many different types of pizzas can you order with 5 toppings

Answer 1

Step-by-step Answer:

Customer is allowed to choose any five, where order does not count.

This means that there are 11 toppings to choose from for the first one, 10 for the second, 9 for the third, 8 for the fourth, and 7 for the last for a total of 11*10*9*8*7 = 11!/6! choices.

Since order does not count, we have over-counted by 5!, so the final answer should be 11!/(6!*5!) choices.

Mathematically, this number is represented by

C(11,5) = 11!/(6!5!) = 462, and is read

"Combination of 5 choices out of 11", or simply "11 choose 5".