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A class has 30 students .We have to form a team of the students including atleast two students and also excluding atleast two students.The number of ways of forming the team is

$\begin{array}{1 1}(A)\;2^n-2n\\(B)\;2^n-2n-2\\(C)\;2^n-2n-4\\(D)\;\text{None of these}\end{array} $

1 Answer

  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
Required number of ways=$nC_2+nC_3+.......+nC_{n-3}+nC_{n-2}$
$\Rightarrow 2^n-(nC_0+nC_1+nC_{n-1}+nC_{n-1}+nC_n)$
$\Rightarrow 2^n-2(n+1)$
$\Rightarrow 2^n-2(n+1)$
$\Rightarrow 2^n-2n-2$
Hence (B) is the correct answer.
answered Jun 20, 2014 by sreemathi.v

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