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1. 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?
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
Solution:
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