CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

CAT Questions | Permutation Probability | Counting Natural No.
× CAT Questions

CAT Quantitative Aptitude
HCF and LCM Factors Remainders Factorials Digits Ratios,Mixtures;Averages Percents; Profits; SICI Speed & Time; Races Logarithms and Exponents Pipes,Cisterns; Work,Time Set Theory Geometry Coordinate Geometry Mensuration Trigonometry Linear & Quadratic Equations Functions Inequalities Polynomials Progressions
CAT Verbal
Para Jumble Sentence Correction Sentence Elimination Paragraph Completion Reading Comprehension Critical Reasoning Word Usage Para Summary Text Completion
CAT LR DI
DI LR: Bar Graphs DI LR: Pie Charts DI LR: Multiple Graphs DI LR: Word Problems DI LR: Line Graphs DI LR: Sequencing DI LR: Grid Puzzles DI LR: Math Puzzles DI LR: Visualization DI LR: Other Patterns DI LR: CAT 2017 Cet DI LR: CAT 2017 Rural Survey DI LR: CAT 2017 Happiness DI LR: CAT 2017 Airlines DI LR: CAT 2017 Travel Route DI LR: CAT 2017 Food Delivery DI LR: CAT 2017 Square Layout DI LR: CAT 2017 Team Project DI LR: CAT 2017 Assets DI LR: CAT 2017 Pizza DI LR: CAT 2017 Electives DI LR: CAT 2017 Chess DI LR: CAT 2017 Dorms DI LR: CAT 2017 Tea DI LR: CAT 2017 Friends DI LR: CAT 2017 Security Scan

CAT Online Coaching
CAT Question MenuCAT Questions

The question is from Permutation and Combination. It is about counting natural numbers. We need to find out the ordered triplets given the sum of three natural numbers. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 1: Sum of three Natural numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?

  1. 45
  2. 36
  3. 54
  4. 28

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: One of our facvourite questions. One of those that get simplified if we think about it the right way, but is extremely tough if you do not get the right line of thought

a + b + c = 10. Now, let us place ten sticks in a row

|       |       |       |       |       |       |       |       |       |

This question now becomes the equivalent of placing two '+' symbols somewhere between these sticks. For instance,
|       |       |       |  +  |       |       |       |       |  +  |

This would be the equivalent of 4 + 5 + 1. or, a = 4, b = 5, c = 1.
There are 9 slots between the sticks, out of which one has to select 2 for placing the '+'s.

The number of ways of doing this would be 9C2. Bear in mind that this kind of calculation counts ordered triplets. (4, 5, 1) and (1, 4, 5) will both be counted as distinct possibilities.
We can also do a + b + c = n where a, b, c have to be whole numbers (instead of natural numbers as in this question) with a small change to the above approach. Give it some thought.

The question is "Sum of three Natural numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?"

Hence the answer is "9C2 = 36."

Choice B is the correct answer.

 


CAT Preparation Online | CAT Permutation and Combination; Probability Videos On YouTube


Other useful sources for Permutation and Combination Questions | Probability Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com