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Q)

From 4 gentlemen and 6 ladies a committee of five is to be be selected.The number of ways in which the committee can be formed.So that gentlemen are in majority is

$\begin{array}{1 1}(A)\;66\\(B)\;156\\(C)\;60\\(D)\;\text{None of these}\end{array} $

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A)
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  • $C(n,r)=\large\frac{n!}{r!(n-r)!}$
In a committee of 5 persons the gentlemen will be in majority if the number of gentlemen $\geq 3$
Total number of ways of forming committee=$4C_3\times 6C_2+4C_4\times 6C_1$
$\Rightarrow 4\times 15+1\times 6$
$\Rightarrow 60+6$
$\Rightarrow 66$
Hence (A) is the correct answer.
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