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

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

Six balls can be selected in the following ways,One red ball and 5 blue ballsOrTwo red balls and 4 blue balls.Total number of ways,= (3C1 × 7C5) + (3C2 × 4C7)
= 63 + 105
= 168

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