Permutations and combinations - Quantitative Aptitude (MCQ) questions for Q. 21060
Q. 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?- Published on 19 Apr 16a. 29
b. 36
c. 48
d. 85
e. None of these
ANSWER: 85
Total balls in a box = 2W + 3B + 5R = 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 = 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.
