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. 105

B. 168

C. 189

D. 120

Answer: Option B

Solution(By Examveda Team)

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