CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

CAT Questions | Permutation Probability | Rearrangement of Letters

The question is from Permutation and Combination. This is about Rearrangement of Letters. Our task is to find the probability of a word satisfying particular condition. 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 18: If all the rearrangements of the word AMAZON are considered, what is the probability that M will feature between the 2As?

  1. \\frac{1}{3}\\)
  2. \\frac{1}{6}\\)
  3. \\frac{2}{5}\\)
  4. \\frac{3}{8}\\)

Online CAT Coaching for CAT 2019


Signup to sample the Best CAT Online Coaching


Video Explanation


Best CAT Coaching in Chennai


Starts Sat, Mar 16, 2019


Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: If you know the different rearrangements of letters in the given word, you are through!!

For this type of question, we need to consider only the internal arrangement within the M and 2As.
M and 2As can be rearranged as AMA, AAM, or MAA.
So, the probability that M will feature between the 2As is \\frac{1}{3}\\).

Now, let us think why we need to consider only the M and 2As.
Let us start by considering a set of words where the M and 2 As are placed at positions 2, 3 and 5.
The other three letters have to be in slots 1, 4 and 6
Three letters can be placed in three different slots in 3! = 6 ways.

Now with __ M A __ A __ there are 6 different words.
With __ A M __ A __ there are 6 different words.
With __ A A __ M __ there are 6 different words.
For each selection of the positions for A,A and M, exactly one-third of words will have M between the two A’s.
This is why only the internal arrangement between A, A and M matters.
So, probability of M being between 2 As is \\frac{1}{3}\\).

The question is "what is the probability that M will feature between the 2As?"

Hence the answer is "\\frac{1}{3}\\)"

Choice A is the correct answer.

 

Online CAT Coaching
Try it free!

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, Mar 23rd, 2019

★ CAT Coaching Info

Best CAT Coaching in Chennai

Sign up for a Free Demo of our CAT Coaching in Chennai

★ Schedule Demo


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,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

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