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

(i) Since, particular player is always chosen. It means that 11-1=10 players are selected out of the
remaining 15-1=14 players,
`therefore`Required of ways`=.^(14)C_(10)=.^(14)C_(4)`
`=(14*13*12*11)/(1*2*3*4)=1001`
(ii) Since, particular player is never chosen. it means that 11 players are seletected out the remaining 15-1=14. players.
`therefore`Required number of ways=`.^(14)C_(11)=.^(14)C_(3)`
`=(14*13*12)/(1*2*3)=364`