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

Calculate the number of possible combinations:

  1. You have a set of 10 objects.  How many different sets of 3 objects can you make (order does not matter)?
  2. You have a set of 6 objects. How many different sets of 5 objects can you make (order does not matter)?
  3. You have a set of 4 objects.  How many different sets of 4 objects can you make (order does not matter)?
  4. 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?
  5. You making a sandwich.  You can choose 5 of 12 different toppings (meats, veggies, etc).  How many different sandwiches can you make?
  6. 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?
  7. In the same ice cream shop, how many different flavered three-scoop cones can you get?
  8. 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?

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