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

$\begin{array}{1 1}(A)\;16C_{11}\\(B)\;14C_9\\(C)\;16C_9\\(D)\;16C_2\end{array} $

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  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
Total no of players =16
Hence we have to select 11 players out of 16
So required no of ways =$11C_{16}$
Since 2 particular players are always included,so we have to select 9 players out of remaining 14 players
This can be done in $14C_9$ ways
$\Rightarrow 14C_9=\large\frac{14!}{9!\times 6!}$
$\Rightarrow \large\frac{14\times 13\times 12\times 11\times 10\times 9!}{91\times 6\times 5\times 4\times 3\times 2\times 1}$
$\Rightarrow 333.66$ ways
Hence (B) is the correct answer.
answered May 15, 2014 by sreemathi.v

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