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A bag contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at most 2 of them are red is
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The correct answer is:
$420$
The required number of ways
$\begin{aligned} & ={ }^7 \mathrm{C}_4+{ }^5 \mathrm{C}_1 \times{ }^7 \mathrm{C}_3+{ }^5 \mathrm{C}_2 \times{ }^7 \mathrm{C}_2 \\ & =35+5 \times 35+10 \times 21 \\ & =35+175+210 \\ & =420\end{aligned}$
$\begin{aligned} & ={ }^7 \mathrm{C}_4+{ }^5 \mathrm{C}_1 \times{ }^7 \mathrm{C}_3+{ }^5 \mathrm{C}_2 \times{ }^7 \mathrm{C}_2 \\ & =35+5 \times 35+10 \times 21 \\ & =35+175+210 \\ & =420\end{aligned}$
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