GMAT Problem Solving- An Urn Contains 6 Red, 4 Blue, 2 Green and 3 Yellow marbles

Question- An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If four marbles are picked up at random, what is the probability that 1 is green, 2 are blue and 1 is red?

1. 13/35
2. 24/455
3. 11/15
4. 1/13
5. 2/455

“An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

It is asked in the question to find what is the probability that out of all marbles 1 is green, 2 are blue and 1 is red?
Let us evaluate further
Total marbles in urn = 6+4+2+3 which is 15..
The Methods to choose 4 of them = 15C4
= \(\frac{15*14*13*12}{4*3*2}\)
= 15 * 7 *13
Same way,
to choose one green, two blues, and one red = 2C1*4C2*6C1
=2*6*6
According to probability
\(\frac{2*6*6}{15*7*13}\)
= \(\frac{24}{455}\)
The answer is 24/455

Correct Answer: C

Model Answer 2

There is another approach to solve this question which is pretty easy
It is given
Total marbles: (6 + 4 + 2 + 3), which is 15.
E shall be the drawing of one green, two blue, and one red marbles.
Then,
n (E) = 2C1*4C2*6C1
= 2 * \(\frac{4*3}{2*1}\) * 6
=72
So n (S) = 15C4
= \(\frac{15*14*13*12}{4*3*2}\)
=1365
Therefore probability will be
P (E) = \(​​\frac{n(E)}{n(S)}\)
=\(\frac{72}{1365}\)
= \(\frac{24}{455}\)
The answer is 24/455

Correct Answer: C

Approach Solution 3:

The inquiry seeks to determine what the likelihood is that out of all the marbles, one is green, two are blue, and one is red.
Let's continue to evaluate.
Total marbles in the urn are 15 (6 + 4 + 2 + 3).
The formulas to select four of these are: 15C4

= \(\frac{15*14*13*12}{4*3*2}\)
= 15 * 7 *13

The methods to select 4 of them are as follows: 15C4 = = 15 * 7 *13
Similarly, to select one green, two blues, and one red, use the formula 2C1*4C2*6C1 = 2*6*6.
Probabilistically speaking.

Correct Answer: C

Suggested GMAT Problem Solving Questions

• GMAT Problem Solving- The two lines are tangent to the circle.
• GMAT Problem Solving- In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one.
• GMAT Problem Solving- In How Many Different Ways can 3 Identical Green Shirts and 3 Identical Red Shirts be Distributed Among 6 Children
• GMAT Problem Solving- The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet
• GMAT Problem Solving- How many factors of 80 are greater than √80?
• GMAT Problem Solving- If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours
• GMAT Problem Solving- If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19
• GMAT Problem Solving- If g is an integer and x is a prime number, which of the following must be an integer?
• GMAT Problem Solving- A store currently charges the same price for each towel that it sells.
• GMAT Problem Solving- What is the value of (\sqrt{7+\sqrt29}-\sqrt{7-\sqrt29})^2
• GMAT Problem Solving- What is the area of a triangle with the following vertices L(1, 3), M(5, 1), and N(3, 5) ?
• GMAT Problem Solving- The product of the five smallest two-digit prime numbers is closest to which of the following powers of 10?
• GMAT Problem Solving- The square of 5^√2 =?
• GMAT Problem Solving- Two adjacent angles of a parallelogram are in the ratio of 1:3. What is the smaller angle of the two?
• GMAT Problem Solving- Which of the following is a perfect cube?
• GMAT Problem Solving- Which of the following represents the largest 4 digit number 
• GMAT Problem Solving- 16 Ounces of Fresh Orange Juice Contains 216 Calories 
• GMAT Problem Solving- What is the remainder when 333^222 is divided by 7?
• GMAT Problem Solving- In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students.
• GMAT Problem Solving- If a Carton Containing a Dozen Mirrors is Dropped