In how many ways a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 are always to be excluded.

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Solution

Team of 11 players out of 25 players
6 - always included
5 - never included
a) Let us select 6 definite players first out of 25 players = 1 way
Remaining to be selected = 5
5 players need to be selected from 25 - 6 - 5 = 14
where 6 - already included players
5 - never included players
$∴^{14} C_{5} = 2002 w a y s$

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