Question

A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw.

[Hint: Required number of ways =³C₁×⁶C₂+³C₂x ⁶C₁+³C₃.]

Answer 1

We know that,

Drawing 1 black and 2 other ball = ³C₁ × ⁶C₂

Drawing 2 black and 1 other ball = ³C₂ × ⁶C₁

Drawing 3 black balls = ³C₃

Number of ways in which at least one black ball can be drawn =

= (1 black and 2 other )or( 2 black and 1 other )or (3 black)

³C₁ × ⁶C₂ + ³C₂ × ⁶C₁ + ³C₃ =3×15+3×6+1

= 45 + 18 + 1

= 64