A box contains 2 white balls and 4 red ball. in how many ways can 3 balls be drawn from the box , if at least one black ball is to be included i the draw ? Pick.
A) 32 B) 48 C) 64 D) 96 E) None
Solution   We have many (1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).   So, Required number of ways = (3 C 1 × 6 C 2) + (3 C 2 × 6 C 1) + (3 C 3)   = ( 3x 6x 5/2x1) + ( 3x 2/2x1x 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 and 4 red ball. in how many ways can 3 balls be drawn from the box , if at least one black ball is to be included i the draw ?