Question: A box contains two white balls, three black balls and four 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?

1. 16
2. 32
3. 64
4. 96
5. 128

Correct Answer: (C)

Solutions and Explanation

Approach Solution - 1 :

There are nine balls total ( 2W, 3B,4R)

The total number of ways to choose 3 balls from a set of 9 balls is 9C3 = (9*8*7) / (3*2*1) = 84
The total number of ways to choose from among the white or red balls when there isn't a black ball already picked = 2W + 4R = 6C3 = 20
Therefore the total number of selection options for three balls with at least one black ball present = 84 -20 = 64

Approach Solution - 2 :

Scenario-1 :

1 Black Ball & 2 Other balls
=> 3c1 * 6c2 = 3*15 = 45

Scenario-2 :

2 Black Balls & 1 Other ball
=> 3c2*6c1 = 3*6 = 18

Scenario-3 :

3 Black Balls
3c3 = 1

As a result, the total number of selection options for three balls with at least one black ball present = 45+18+1 = 64.

“A box contains two white balls, three black balls and four red balls” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

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