There was a pizza parlor that offered six meat toppings and three cheese toppings. How many different combinations can be made if two meat toppings and one cheese toppings are selected?

choose 2 of the 6 meats and one of the 3 cheeses

number of combinations
= C(6,2) x C(3,1)
= 15(3)
= 45

To calculate the number of different combinations that can be made when selecting two meat toppings and one cheese topping, we can use the concept of combinations.

First, let's find the number of combinations for the meat toppings. Since we are choosing two out of six meat toppings, we can use the formula for combinations: C(n, r) = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items we want to choose.

For the meat toppings, we have n = 6 (total number of meat toppings) and r = 2 (number of meat toppings we need to choose). Plugging these values into the formula, we have:

C(6, 2) = 6! / (2! * (6 - 2)!) = 6! / (2! * 4!) = (6 * 5 * 4!) / (2 * 1 * 4!) = (6 * 5) / (2 * 1) = 15

Therefore, there are 15 different combinations for selecting two meat toppings.

Now, let's calculate the number of combinations for the cheese toppings. We have n = 3 (total number of cheese toppings) and r = 1 (number of cheese toppings we need to choose). Plugging these values into the formula, we have:

C(3, 1) = 3! / (1! * (3 - 1)!) = 3! / (1! * 2!) = (3 * 2 * 1) / (1 * 1 * 2) = 3

Therefore, there are 3 different combinations for selecting one cheese topping.

To find the total number of different combinations, we need to multiply the number of meat topping combinations by the number of cheese topping combinations:

Total combinations = 15 * 3 = 45

Therefore, there are 45 different combinations that can be made when selecting two meat toppings and one cheese topping.