In how many ways can a cricket team be selected from a group of 25 players containing 10 batsmen, 8 bowlers, 5 all-rounders and 2 wicketkeepers, assuming that the team of 11 players requires 5 batsmen, 3 all-rounders, 2 bowlers and 1 wicketkeeper?

A team of 11 players is to be made from 25 players.


selecting 5 batsmen from 10 in 10C5 ways.


selecting 3 all-rounders from 5 in 5C3 ways.


selecting 2 bowlers from 8 in 8C2 ways.


selecting 1 wicketkeeper from 2 in 2C1 ways.


Thus , by the multiplication principle, we get


= 10C5 8C2 5C32C1 ways


Applying nCr =


= 141120 ways


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