How many ways can a captain and a vice-captain be selected from a team of $11$ players?

To fill the post of captain, we can choose any $1$ player out of the $11$ available positions ($11$ choices).
Once the captain is selected, $10$ players remain. Any $1$ of these $10$ remaining players can be chosen as the vice-captain ($10$ choices).

Using the fundamental counting principle, the total number of ways is:

$$\text{Total ways}=11\times 10=110$$