# Combinations (Making sets, of a certain size, from another set)

Calculate the number of possible combinations:

- You have a set of 10 objects. How many different sets of 3 objects can you make (order does not matter)?
**n=10, r=3; 120 combinations** - You have a set of 6 objects. How many different sets of 5 objects can you make (order does not matter)?
**n=6, r=5; 6 combinations** - You have a set of 4 objects. How many different sets of 4 objects can you make (order does not matter)?
**n=4, r=4; 1 combination** - You are shopping for t-shirts. The store has 5 different colors. You are buying 3 different colored shirts. How many different combinations of shirts can you choose?
**n=5, r=3; 10 combinations** - You making a sandwich. You can choose 5 of 12 different toppings (meats, veggies, etc). How many different sandwiches can you make?
**n=12, r=5; 792 sandwiches** - In an ice cream shop, there are 20 possible ice cream flavors. You are getting a double scoop cone (you must choose two different flavors). How many different cones can you get?
**n=20, r=2; 190 cones** - In the same ice cream shop, how many different flavered three-scoop cones can you get?
**n=20, r=3; 1140 cones** - In that same ice cream shop, if you can also choose from 2 different types of cones (sugar or cake), how many possible three-scoop cones can you get?
**n=20, r=3, times 2 types of cones; 2280 cones**