Home




Dividing Objects into Groups - GMAT Combinations

GMAT Permutation and Combination - Dividing Objects into GroupsDivision of Objects into Groups: The GMAT sometime tends to surprise test-takers with questions on little-known topics. Although the topic of combinations is a widely known and studied topic, a sub-topic within combinations that is sometimes neglected by a significant number of test takers is that of division of objects into groups.

The number of ways to divide m+n+p objects into three groups having m,n, and p objects is (m+n+p)!/(m! n!  p!)

Example: In how many ways can you divide 28 schoolchildren into three groups having 3,5, and 20 children?

Solution: The answer is simply 28!/(3!5!20!)

This problem type is simple enough. However, the GMAT can try to trick you by asking you a subtle variant of this type of problem.

The number of ways to divide m+2n objects into three groups having m,n, and n objects is (m+2n)!/m! x n! x n! x (no. of groups having the same number of objects)!

Example: In how many ways can you divide 28 schoolchildren into three groups having 4,12, and 12 children?

Solution: The answer is NOT 28!/(4!12!12!)

Instead, we must divide by 2! to get the answer as 28!/(4!12!12!2!)

Why do we divide by 2! in this case?

The reason is that two groups have the same number of objects to be placed in them. Therefore whether we select an object for one of these two groups or the other, the selection is essentially the same. Therefore we must divide by the factorial of the number of groups of the same size in order to account for the extra counting.

Is that it then? No – the GMAT has one last trick up its sleeve.

The number of ways to divide m+n+p objects into three groups having m,n, and p objects, where each group has a specific name assigned to it, is (m+n+p)! x (number of arrangements of the given names)/m! x n! x p!  

Example: In how many ways can you divide 28 schoolchildren into three groups having 3,5, and 20 children and being given the names A,B, and C?

Solution: The answer is now 28! x 3!/(5! x 20!)

Why do we multiple by 3! Here?
Remember, the three names A,B,C can be assigned to the three groups having 3,5, and 20 children in any way.

For instance, we can have A = group with 3 children, B = group with 5 children, C = group with 20 children

OR

A = group with 5 children, B = group with 3 children, C = group with 20 children

To account for the fact that any of the three names can be assigned to any group, we must multiple with the number of arrangements possible for the names.

To round off the discussion, here is a final example:

Example: In how many ways can you divide 28 schoolchildren into three groups having 3,5, and 20 children and being given the names A,B, C, and D?

Solution: The answer is now 28! x 4C3 x 3!/(5! x 20!)

Author : 

Gyan One
GyanOne is an educational services firm focused on premium GMAT coaching, application advisory (with a focus on ISB applications), and interview preparation for B-school admissions. GyanOne operates in the New Delhi region of India and has top global B-school alumni with a minimum score of 770 on the GMAT, as instructors. All GyanOne counsellors are professionally trained top B-school alumni with an experience of 100+ MBA applications behind them.

Essential GMAT Reading Comprehension Guide


After you read F1GMAT’s Essential GMAT Reading Comprehension Guide, you will:

1. Complete GMAT RC Questions in less than 1 minute and 50 seconds

2. Read Faster

3. Take Notes Effectively

4. Collect and Interpret Facts

5. Speed up Summary Creation

6. Remember Information

7. Question the Author   

8. Learn to answer GMAT Reading Comprehension Title question   

9. Learn to Solve GMAT Reading Comprehension Main Idea Question   

10.Learn to Solve GMAT Reading comprehension inference question   

11. Learn to Solve GMAT Reading Comprehension Detail Questions   

12. Learn to Organize passage in GMAT Reading Comprehension   

13. Learn to Identify style/tone or attitude of the author

14. Learn to Improve GMAT Reading Comprehension Score


Download Essential GMAT Reading Comprehension Guide



Mastering GMAT Critical Reasoning



After you read F1GMAT’s Mastering GMAT Critical Reasoning Guide, you will:

1) Learn to eliminate out of scope answer choices

2) Learn to spot logical fallacies

3) Learn to read questions by focusing on the holy trinity – premise, assumption, and conclusion.

4) Learn to disregard filler information

5) Complete GMAT CR Questions in less than 1 minute and 40 seconds


Download Mastering GMAT Critical Reasoning




Navigate F1GMAT


F1GMAT Services (MBA Applicants) 


MBA Research

MBA Salary(Latest Salary Data)
 
MBA Admission Interview Tips

Funding 

Deadlines

MBA Application Essays

GMAT Tutorials (Free)


GMAT Question Bank

Top MBA Programs


Get F1GMAT's Newsletters (Best in the Industry)
Included in the Newsletter:

  • Ranking Analysis
  • Post-MBA Salary Trends
  • Post-MBA Job Function & Industry Analysis
  • Post-MBA City Review
  • MBA Application Essay Tips
  • School Specific Essay Tips
  • GMAT Preparation Tips
  • MBA Admission Interview Tips
  • School Specific Interview Tips
  • Funding Guidance and
  • Special Consultation Service (only for Subscribers)

Subscribe to F1GMAT's Newsletter