A box contains two white, three black and four red balls. In how many

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

Answer»

There are two white, three black and four red balls.

We have to draw 3 balls, out of these 9 balls in which at least one black ball is included.

So we have following possibilities:

Black balls	1	2	3
Other than black	2	1	0

.’. Number of selections = ³C₁ x ⁶C₂ + ³C₂ x⁶C₃ + ³C₃ x ⁶C₀

= 3×15+ 3×6+1= 45+ 18 + 1= 64