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# How many committee of five persons with a chairperson can be selected from 12 persons

$\begin{array}{1 1}(A)\;3940\\(B)\;3950\\(C)\;3960\\(D)\;3970\end{array}$

Can you answer this question?

The chair person can be selected in =12 ways
The ways of selecting the other 4 members=$11C_4$
$\Rightarrow 11C_4=\large\frac{11!}{4!\times 7!}$
$\Rightarrow \large\frac{11\times 10\times 9\times 8\times 7!}{4\times 3\times 2 \times 1\times 7!}$
$\Rightarrow 110\times 3$
$\Rightarrow 330$
No of ways of selecting 5 member of the committee=$330\times 12$
$\Rightarrow 3960$
Hence (C) is the correct answer.
answered May 15, 2014