# Questionbank: Permutation and Probability

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If you know the different rearrangements of letters in the given word, you are through!!

## Rearrangement of Letters - Probability

Q.18: If all the rearrangements of the word AMAZON are considered, what is the probability that M will feature between the 2As?
1. 1/3
2. 1/6
3. 2/5
4. 3/8

Choice A. 1/3

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## Detailed Solution

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 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 1/3.

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