The local pizzeria is advertising a special where you can get a large pizza with up to 3 different toppings for only $10. If the pizzeria offers 11 different toppings, how many different types of pizza can you get in this special deal?
C(11,3) = 11*10*9/6
C(11,0) + C(11,1) + C(11,2) + C(11,3)
the problem says "up to 3"
To find the number of different types of pizza you can get in this special deal, we need to calculate the number of combinations for choosing up to 3 toppings out of 11.
The number of combinations can be found using the formula for combinations: C(n, r) = n! / (r! * (n - r)!)
In this case, n = 11 (number of available toppings) and r = 3 (maximum number of toppings allowed). Plugging these values into the formula, we get:
C(11, 3) = 11! / (3! * (11 - 3)!)
Calculating this expression step by step:
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800
3! = 3 * 2 * 1 = 6
(11 - 3)! = 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
Now let's substitute these values back into the formula:
C(11, 3) = 39,916,800 / (6 * 40,320)
Cancelling out common terms:
C(11, 3) = 39,916,800 / 242,880
Simplifying the division:
C(11, 3) = 165
Therefore, you can get 165 different types of pizza in this special deal, considering the available 11 toppings and choosing up to 3 different toppings.