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) The total number of ways of selecting 11 players out of 15 is `""^(15)C_(11)`
`=(15xx14xx13xx12)/(4xx3xx2xx1)=1365`
(ii) if two particular players are always chosen. This means that 9 players are selected out of the remaining 13 players.
`therefore ` Required number of ways =`""^(13)C_(9)`
`=(13xx12xx11xx10)/(4xx3xx2xx1)=715`
(iii) If two particular players are never chosen. This means that 11 players are selected out of the remaining 13 players.
`therefore ` Required number of ways =`""^(13)C_(11)`
`=(13xx12)/(2xx1)=78`