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True-or-False:A candidate is required to answer 7 questions out of 12 questions which are divided into two groups,each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array} $

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Total no of questions =12
Questions required to Ans =7
Two groups $\rightarrow 6-6$
No of ways =$6C_5\times 6C_2+6C_2\times 6C_5+6C_3\times 6C_4+6C_4\times 6C_3$
$6C_2=\large\frac{6!}{2!4!}=\frac{6\times 5}{2}$$=15$
$6C_3=\large\frac{6!}{3!3!}=\frac{6\times 5\times 4\times 3!}{3!\times 3\times 2}$$=20$
$6C_4=\large\frac{6!}{4!2!}=\frac{6\times 5\times 4!}{4!\times 2}$$=15$
No of ways =$6\times 15+15\times 6+20\times 15+15\times 20$
$\Rightarrow 90+90+300+300$
$\Rightarrow 180+600$
$\Rightarrow 780$ ways
Hence the given statement is false
answered May 16, 2014 by sreemathi.v

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