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Question

A village has $$10$$ players. A team of $$6$$ players is to be formed. $$5$$ members are chosen first out of these $$10$$ players and then the captain from the remaining players. Then the total number of ways of choosing such teams is


A
1260
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B
210
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C
(10C6)5!
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D
10C56
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Solution

The correct option is A $$1260$$
A village has $$10$$ players.
Now a team of $$6$$ players is to be formed.
Thus $$1^{st}$$ we select the $$5$$ players from total $$10$$ players in $${ _{  }^{ 10 }{ C } }_{ 5 }$$ ways and $$6^{th}$$ person will select from the remaining $$5$$ players in $$5$$ ways.
Total number of ways $$={ _{  }^{ 10 }{ C } }_{ 5 }\times 5=1260$$

Mathematics

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