Problema Solution
The local pizza parlor has 15 choices of toppings for a pizza. What is the maximum number of pizzas you could order with a different combination of two toppings each?
Answer provided by our tutors
Since the order of the selected toppings is not important we need to find the number of 2-combination of a given set of 15 elements.
We use the formula for k-combinations from a set of n elements:
C(n, k) = n!/(k!(n - k)!, where n! = 1*2*3*...*(n - 1)*n
In our case n = 15 and k = 2
C(15, 2) = 15!/(2!13!)
C(15, 2) = 14*15/2
C(15, 2) = 105
The maximum number of different pizzas you could order is 105.