A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw	Choose one:  A) 64  B) 128  C) 132  D) 222  E) None of these
Explanation:   From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that   at least one black ball should be there.   Hence we have 3 choices   64ll three are black   Two are black and one is non black   One is black and two are non black   Total number of ways   = 3C3 + (3C2 x 6C1) + (3C1 x 6C2) [because 6 are non black]   =1+[3×6]+[3×(6×5/2×1)]=1+18+45= 
<gadget id="calculator">1+18+45</gadget>
<output>64</output>
64   Option 64
<result>A</result>
A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw