Final answer:
Karen can choose 3 pizza toppings from a menu of 16 toppings in 560 different ways, using the combinations formula in combinatorics.
Step-by-step explanation:
The question at hand asks how many ways Karen can choose 3 pizza toppings from a menu of 16 toppings. This is a problem of combinatorics, a field of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. To solve this, we can use the combinations formula which is given by nCr = n! / (r!(n-r)!), where 'n' is the total number of items to choose from, 'r' is the number of items to choose, 'n!' (n factorial) is the product of all positive integers up to n, and 'r!' and '(n-r)!' are defined similarly.
In this case, we have 16 toppings (n=16) and we want to choose 3 of them (r=3), so we use the formula to calculate the number of combinations:
16C3 = 16! / (3!(16-3)!) = 16! / (3!13!) = (16 × 15 × 14) / (3 × 2 × 1) = 560
Therefore, Karen can choose her 3 pizza toppings in 560 different ways.