Question

A box contains 12 balls out of which 4 are red and rest are blue. In how many ways can a random sample of 5 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 5 balls of the same colour?

• A. ⁴C₂ x ⁸C₃ + ⁴C₁ x ⁸C₄
• B. ⁴C₁ x ¹¹C₄ + ⁴C₁ x ⁸C₄
• C. ⁴C₂ x ¹⁰C₂ + ⁴C₁ x ¹⁸C₅
• D. None of these

Answer 1

The correct option is A

⁴C₂ x ⁸C₃ + ⁴C₁ x ⁸C₄

The number of ways that it can be done = ${}^4{C}_2{\times }^8{C}_3$+${}^4{C}_1{\times }^8{C}_4$