Question

how many ways can Aileen choose 2 pizza toppings from a menu of 19 toppings if each topping can be chosen once ?

Answer 1

`171\text{ ways}`

Expalnation:

From what we have here, there are 19 toppings to choose from

To choose the first topping, there are 19 choices to select from

For the second topping selected, since repetition is not allowed, there would be 17 toppings to choose from

Thus, the total number of ways will be according to the combination rule as follows:

`\begin{gathered} ^nC_r\text{ = }(n!)/((n-r)!r!) \\ ^(19)C_2\text{ = }(19!)/((19-2)!2!)\text{ = 171 ways} \end{gathered}`