Question

Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ___________.

Answer 1

Number of red balls = 5
Number of white balls = 4
Number of black balls = 3
Number of ball drawn = 3
Note, at-least 2 red balls can be drawn in following ways
→ 2 red and 1 non red.
→ all 3 reds balls.
∴ Number of ways of drawing at-least two red balls is all red ⁵C₃ + ⁵C₂ × 7C₁ $$\begin{gathered} =\frac{4\times 5}{2}+\frac{4\times 5}{2}\times 7 \\ =10+35\times 2 \\ =80 \end{gathered}$$