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?
Pick one:  A) 32  B) 48  C) 64  D) 96  E) None of these
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 (6x5)/(2x1)] + [(3x2)/(2x1) x 6] + 1 = 45 +18 + 1= 
<gadget id="calculator">45 +18 + 1</gadget>
<output>64</output>
64.   Answer 64.
<result>C</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?