It's been a long week, and you decide you need some ice cream. Your roommate is going to the store, so you hand her some cash and ask her to pick up some ice cream. When she asks what flavors you want, you reply that any Ben & Jerry or Eddy would be great. You tell her to pick up at least $2$ cartons... It's been that kind of week.

The super market offers $10$ Ben & Jerry flavors and $5$ Eddy flavors. When your roommate comes back with a bag of ice cr$$am cartons, how many total combinations are possible?

Out of the $2$ cartons your roommate bought, suppose she got you $1$ Ben & Jerry carton. How many different ways are there for her to pick $1$ Ben & Jerry carton?

This leaves

cartons that

must be Eddy. How many different ways are there for her to pick that many Eddy cartons?

In total, how many different bags of ice cream does this yield?

Thus, what is the probability of this type of bag of ice cream cartons? $($Enter the probability as a fraction.$)$

Suppose your roomate got you all Ben & Jerry cartons. How many different ways are there for her to pick all Ben & lerry cartons?

This leaves cartons that must be Eddy. How many different ways are there for her to pick that many Eddy cartons?

In total, how many different