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 ___________.
Solution:
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.
$\therefore$ Number of ways of drawing at-least two red balls is all red $\underline{5} \underline{C}_{3}+{ }^{5} C_{2} \times 7 C_{1}$
$=\frac{4 \times 5}{2}+\frac{4 \times 5}{2} \times 7$
$=10+35 \times 2$
$=80$