Answer
$283$ people liked to ski or snowboard.
Work Step by Step
If $A$ is the set of people who liked to ski, and $B$ is the set of people who liked to snowboard, then:
$n(A)=178$ people liked to ski.
$n(B)=154$ people liked to snowboard.
$n(A\cap B)=49$ people liked to ski and snowboard.
The formula for cardinality of the union of two sets:
$n(A\cup B)=n(A)+n(B)-n(A\cap B)$
$n(A\cup B)=178+154-49=283$
$283$ people liked to ski or snowboard.
