A local pizza shop has 8 different toppings to pick from. How many ways can you pick three different toppings for your pizza if order does not matter?
To find the number of ways to pick three different toppings for your pizza, given that the order does not matter, you can use the combination formula. The combination formula, also known as "n choose k," is expressed as:
C(n, k) = n! / (k! * (n-k)!)
Where n is the total number of toppings available and k is the number of toppings to be chosen. In this case, n = 8 (the total number of toppings available) and k = 3 (the number of toppings to be chosen).
So, to find the number of ways to pick three different toppings for your pizza, we can substitute these values into the combination formula:
C(8, 3) = 8! / (3! * (8-3)!)
Calculating this, we have:
C(8, 3) = 8! / (3! * 5!)
= (8 * 7 * 6 * 5!)/ (3! * 5!)
= (8 * 7 * 6) / (3 * 2 * 1)
= 56
Therefore, there are 56 different ways to pick three different toppings for your pizza when the order does not matter.