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Q)

# A box contain 2 white balls,3 black balls and 4 red balls.The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is

$\begin{array}{1 1}(A)\;60\\(B)\;62\\(C)\;64\\(D)\;66\end{array}$

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A)
• $c(n,r)=\large\frac{n!}{r!(n-r)!}$
$\Rightarrow 3C_1\times 6C_2+3C_2\times 6C_1+3C_3\times 6C_0$
$\Rightarrow 45+18+1$
$\Rightarrow 64$