In a group of 20 friends, 11 like to ski, 13 like to snowboard, and 3 do not like to do either. How many of the friends like to both ski and snowboard?
Let $x$ be the number of friends who like to both ski and snowboard.

Then $11-x$ of the friends like to ski but not do not like to snowboard, and $13-x$ of the friends like to snowboard but do not like to ski.

Since 3 of the 20 friends do not like to ski or snowboard, then 17 like to either ski or snowboard or both.

Thus, $(11-x)+(13-x)+x=17$ and so $x=7$.

Therefore, 7 of the friends like to both ski and snowboard.

ANSWER: 7