A box contains 2 white, 3 black and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?	Choose the correct option.
A) 85	B) 66	C) 27	D) 19	E) 17
Explanation:   Total balls in a box = 2W + 3B + 5R = 10 balls.   Therefore total number of ways of drawing 3 balls from 10 balls is 10C3 2  + 3  + 5= 
<gadget id="calculator">2  + 3  + 5</gadget>
<output>10</output>
10 balls.   Therefore total number of ways of drawing 3 balls from 10 balls is 10C3= 120 ways ........(1)   This includes all types of color combinations of white, black and red.   Now total balls in a box of white and red color = 2W + 5R = 7 balls.   Therefore total number of ways of drawing 3 balls from 7 balls is 7C3 2  + 5= 
<gadget id="calculator">2  + 5</gadget>
<output>7</output>
7 balls.   Therefore total number of ways of drawing 3 balls from 7 balls is 7C3= 35 ways ........(2)   This includes all types of color combinations of white and red only.   Therefore from (1) and (2), we get the total number of ways of drawing 3 balls, which includes at least one black ball = 120 – 35 = 85 ways.   85NSWER: 85
<result>A</result>
A box contains 2 white, 3 black and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?