A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
Choose the correct choice from the following answers.
A) 54	B) 58	C) 62	D) 64	E) 68
We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).   Required number of ways	= (3C1 x 6C2) + (3C2 x 6C1) + (3C3)   = 3 x	6 x 5 + 3 x 2	x 6 + 1   2 x 1	2 x 1   = (45 + 18 + 1)= 
<gadget id="calculator">(45 + 18 + 1)</gadget>
<output>64</output>
64   Answer: 64.
<result>D</result>
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?