CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

CAT Questions | Permutation Probability | Counting Natural No.

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