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A bag contains 10 marbles out of which 3 are red and the rest are blue. In how many ways can a random sample of 6 marbles be drawn from the bag so that at the most 2 red marbles are included in the sample and no sample has all the 6 marbles of the same colour?

A bag contains 10 marbles out of which 3 are red and the rest are blue. In how many ways can a random sample of 6 marbles be drawn from the bag so that at the most 2 red marbles are included in the sample and no sample has all the 6 marbles of the same colour? Correct Answer 168

Explanation:

Possible ways are as follows:

  • 1 red marble out of the three and 5 blue marbles out of the seven.
  • 2 red marbles out of the 3 and 4 blue marbles out of the seven.

∴ The total number of ways in which a random sample of six marbles can be drawn.

3C1 × 7C5 + 3C2 × 7C4 = 168 

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