In how many ways can a cricket eleven be chosen out of a batch of 15 players, if
(i) there is no restriction on the selection ?
(ii) a particular player is always chosen?
(iii) a particular player is never chosen?

Explanation

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

### Part (i): No restriction on the selection
When there are no restrictions, we need to choose 11 players from 15. The number of ways to choose r items from n items is given by the combination formula:

\[ \text{Number of ways} = \binom{n}{r} = \frac{n!}{r!(n - r)!} \]
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