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. 

∴ Number of ways of drawing at-least two red balls is all red 5C5C2 × 7C1           

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

$=10+35 \times 2$

$=80$

 

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