# Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls.

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 $\underline{5} \underline{C}_{3}+{ }^{5} C_{2} \times 7 C_{1}$

$=\frac{4 \times 5}{2}+\frac{4 \times 5}{2} \times 7$

$=10+35 \times 2$

$=80$