Argentina had football team of 22 player of which captain is from brazilian team and goalki from european team. for remaining player they have picked 6 from argentinean and 14 from european. now for a team of 11 they must have goalki and captain so out of 9 now they plan to select 3 from argentinean and 6 from european. find out number of methods available for it.
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Total players = 22
Team we need to select = 11 players
Fixed players = 2 i.e Captain and Goalki
Remaining players we need to select = 9
Lot of players we can select from = 6 Argentinean, 14 European
We need to select = 3 Argentinean, 6 European
So, ways to select such a team will be given by
For 3 Argentinean from 6, we can select in =
⁶C₃ ways = 6!/(3!)(3!) = 20 ways
For 6 European from14, we can select in =
¹⁴C₆ ways = 14!/(8!)(6!) = 3003 ways
So, to select such 9 players, we have ways = 20 x 3003 = 60060 ways
Therefore, we can select such a team in 60060 ways.
Team we need to select = 11 players
Fixed players = 2 i.e Captain and Goalki
Remaining players we need to select = 9
Lot of players we can select from = 6 Argentinean, 14 European
We need to select = 3 Argentinean, 6 European
So, ways to select such a team will be given by
For 3 Argentinean from 6, we can select in =
⁶C₃ ways = 6!/(3!)(3!) = 20 ways
For 6 European from14, we can select in =
¹⁴C₆ ways = 14!/(8!)(6!) = 3003 ways
So, to select such 9 players, we have ways = 20 x 3003 = 60060 ways
Therefore, we can select such a team in 60060 ways.
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