A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

A team of 6 members has to be selected from the 10 players. This can be done in  $10C6$ or 210 ways. 

Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 210×6= 1260