Erica started her own pizza restaurant. She offers one type of crust, one kind of sauce and 6 different toppings: sausage, pepperoni, mushroom, onions, green peppers and tomatoes.
How many different two-topping pizzas can she make?
My guess is 30.
Guessing doesn't help, Sydney.
6 topping choices, 2 toppings per pizza: 6 choose 2, which is 6!/(2!4!)
To calculate the number of different two-topping pizzas Erica can make, we can use the concept of combinations. A combination is a selection of items without regard to the order in which they are selected.
In this case, Erica has 6 different toppings to choose from, and she needs to select two of them for each pizza. The formula for calculating combinations is given by:
C(n, r) = n! / (r!(n-r)!)
where "n" is the total number of items to choose from (in this case, 6 toppings), and "r" is the number of items to be chosen (2 toppings).
So, using this formula, we can calculate the number of different two-topping pizzas Erica can make:
C(6, 2) = 6! / (2!(6-2)!)
= 6! / (2! * 4!)
= (6 * 5 * 4!) / (2! * 4!)
= (6 * 5) / 2!
= 30 / 2
= 15
Therefore, Erica can make 15 different two-topping pizzas using the given toppings.