How many ways can Aileen choose 5 pizza toppings from a mean of 19 toppings if can only be chosen once?

11628

To find the number of ways Aileen can choose 5 pizza toppings from a menu of 19 toppings, we can use the concept of combinations. In this problem, order does not matter, and repetitions are not allowed because each topping can only be chosen once.

To calculate the number of combinations, we can use the formula for combinations, which is:

C(n, r) = n! / (r! * (n - r)!)

Here, n represents the total number of items (19 toppings) and r represents the number of items chosen (5 toppings).

Using the formula, we can calculate the number of ways Aileen can choose 5 pizza toppings:

C(19, 5) = 19! / (5! * (19 - 5)!)

Simplifying the equation:

C(19, 5) = 19! / (5! * 14!)

Now, let's calculate the factorial terms:

19! = 19 * 18 * 17 * 16 * 15 * 14!

5! = 5 * 4 * 3 * 2 * 1

Simplifying further:

C(19, 5) = (19 * 18 * 17 * 16 * 15 * 14!) / (5 * 4 * 3 * 2 * 1 * 14!)

Canceling out the common factor of 14!:

C(19, 5) = (19 * 18 * 17 * 16 * 15) / (5 * 4 * 3 * 2 * 1)

Evaluating the expression:

C(19, 5) = 116,280

Therefore, Aileen can choose 5 pizza toppings from 19 toppings in 116,280 different ways.