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# Find the number of ways of selecting 9 balls from 6 red balls,5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

$\begin{array}{1 1}(A)\;1000\\(B)\;1500\\(C)\;2000\\(D)\;2500\end{array}$

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A)
• $C(n,r)=\large\frac{n!}{r!(n-r)!}$
The number of ways of selecting 3 red balls out of 6 red balls =$6C_3$
The number of ways of selecting 3 white balls out of 5 white balls =$5C_3$
The number of ways of selecting 3 blue balls out of 5 blue balls =$5C_3$
$6C_3\times 5C_3\times 5C_3=6C_3\times 5C_2\times 5C_2$
$\Rightarrow \large\frac{6\times 5\times 4}{1\times 2\times 3}\times \frac{5.4}{1\times 2}\times \frac{5.4}{1.2}$
$\Rightarrow 20\times 10\times 10$
$\Rightarrow 2000$