A pizza company has 15 toppings to choose from
A. One topping is anchovies. How many different 3 topping pizzas do not include anchovies?
B. There are 6 vegetable toppings. How many different 3 topping pizzas have no vegetables?
C. How many different 3 topping pizzas have at least one vegetable?
To answer these questions, we can use combinations.
A. To find the number of different 3-topping pizzas that do not include anchovies, we need to choose 3 toppings out of the remaining 14 (since one topping is already fixed as anchovies).
We can use the formula for combinations: nCr = n! / (r! * (n-r)!)
So, the number of different 3-topping pizzas without anchovies is 14C3 = 14! / (3! * (14-3)!) = 14! / (3! * 11!)
B. To find the number of different 3-topping pizzas that have no vegetables, we need to choose 3 toppings out of the remaining 15 - 6 = 9 (since there are 6 vegetable toppings).
Again, we can use the combinations formula: 9C3 = 9! / (3! * (9-3)!)
C. To find the number of different 3-topping pizzas that have at least one vegetable, we can subtract the number of pizzas with no vegetables from the total number of pizzas (which can be found by choosing 3 out of 15 toppings).
So, the number of different 3-topping pizzas with at least one vegetable is 15C3 - 9C3 = 15! / (3! * (15-3)!) - 9! / (3! * (9-3)!)
Hopefully, this helps you find the answers to your questions!