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In how many ways can a cricket team of 11 players be chosen out of a batch of 15 players?
- There is no restriction on the selection.
- A particular player is always chosen.
- A particular player is never chosen.
(i) Number of ways choosing 11 players from 15 is 15C11 = 15C4
`= (15 xx 14 xx 13 xx 12)/(4 xx 3 xx 2 xx 1)`
= 15 × 7 × 13
= 1365.
(ii) If a particular is always chosen there will be only 14 players left put, in which 10 are to selected in 14C10 ways.
14C10 = 14C4
`= (14xx13xx12xx11)/(4xx3xx2xx1)`
`= (14 xx 13 xx 11)/2`
= 91 × 11
= 1001 ways
(iii) If a particular player is never chosen we have to select 11 players out of remaining 14 players in 14C11 ways.
i.e., 14C3 ways = `(14 xx 13 xx 12)/(3xx2xx1)` = 364 ways.
Is there an error in this question or solution?