In how many ways can a cricket team of eleven players be chosen out a batch 15 players, if (i) a particular is always chosen. (ii) a particular player is never chosen?

Explanation

To solve the problem of selecting a cricket team of eleven players from a batch of 15 players under two different conditions, we can break it down into two parts.

### Part (i): A Particular Player is Always Chosen

1. **Identify the total players and the chosen player**: We have 15 players in total, and one particular player is always chosen. This means we are left with 14 players to choose from.

2. **Determine how many more players need to be selected**: Since one player is already chosen, we need to select 10 more players to complete the team of 11.

...