A bag contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4…

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
  1. $385$
  2. $406$
  3. $210$
  4. $420$

Solution

The required number of ways $\begin{aligned} & ={ }^7 \mathrm{C}_4+{ }^5 \mathrm{C}_1 \times{ }^7 \mathrm{C}_3+{ }^5 \mathrm{C}_2 \times{ }^7 \mathrm{C}_2 \\ & =35+5 \times 35+10 \times 21 \\ & =35+175+210 \\ & =420\end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 2)

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