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

Answer: Option A

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

Alternatively
We can select the 5 member team out of the 10 in ¹⁰C₅ ways = 252 ways.
The captain can be selected from amongst the remaining 5 players in 5 ways.
Therefore, total ways the selection of 5 players and a captain can be made,
= 252 × 5
= 1260