# Combination

#### Hasan

##### New Member
You are at an ice cream shop that offers 9 different flavors of ice cream. A large ice cream cone comes with three scoops of ice cream. You can choose an ice cream cone with any combination of flavors for the three scoops: all three scoops can be the same flavor, two of the three can be the same flavor, or all three scoops can be different flavors. If the order in which the flavors are placed onto the ice cream cone is important, what is the total number of ways to construct a large ice cream cone?

#### Dason

Hi! :welcome: We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

My approach

9!/(6!*3!)= 84

Is it correct?

#### Hasan

##### New Member
all the three same two same and one is different all the three are different

9*1*1 + 9*8*1 + 9*8*7 = 9+72+504=585

Is this solution correct?