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

(i) Total number of ways of selecting 11 players out of 15
`=.^(15)C_(11)=.^(15)C_(15-11)=.^(15)C_(4)=(15xx14xx13xx12)/(4xx3xx2xx1)=1365`.
(ii) When a particular player is always chosen, then we will have to choose 10 players out of remaining 14.
`:.` required number of ways
`=.^(14)C_(10)=.^(14)C_(14-10)=.^(14)C_(4)=(14xx13xx12xx11)/(4xx3xx2xx1)=1001`.
(iii) When a particular player is never chosen, then we will have to choose 11 players out of remaining 14.
`:.` required number of ways
`=.^(14)C_(11)=.^(14)C_(14-11)=.^(14)C_(3)=(14xx13xx12)/(3xx2xx1)=364`.