Question

In how many ways can a football team of $11$ players be selected from $16$ players? How many of these will Include $2$ particular players?

• A. $4638,2020$
• B. $4658,2001$
• C. $4368,2002$
• D. None of these

Answer 1

The correct option is C $4368,2002$

$11$ players can be selected of $6$ in ${}^{16}{C}_{11}$ ways

$\Rightarrow \frac{16!}{11!(16-11)!}=4368$ ways

Including $2$ particular players

if two particular players is to included selection will be ${}^{14}{C}_9$

$\Rightarrow \frac{14!}{9!(14-9)!}\Rightarrow \frac{14\times 13\times 12\times 11\times 10\times 9!}{9!5\times 4\times 3\times 2}\Rightarrow 2002$