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True-or-False:To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes.If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all,the number of ways in which the selection can be made is $5C_3\times 20C_9$

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

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  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
No of vacancy =12
No of candidate =25
Total no of seats of SC=5
Reserved for SC=3
No of ways of filling 3 reserved vacancies by 5 scheduled caste candidates =$5C_3$
No of ways of filling rest 9 vacancies by 22 candidates =$22C_9$
$\therefore$ Required no of ways of filling vacancies =$5C_3\times 22C_9$
Hence the given statement is false.
answered May 19, 2014 by sreemathi.v

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