Question:

If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning, which one of the following is 19th word ?

Updated On: Apr 8, 2025
  • KAMS
  • AKMS
  • SAMK
  • AMSK
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The Correct Option is C

Approach Solution - 1

To find the 19th word in the dictionary order of all permutations of the letters in the word "MASK," we need to arrange the letters in alphabetical order and determine the word at the 19th position.
The alphabetical order of the permutations is as follows:
AKMS
AMSK
KAMS
KASM
KSAM
KSMA
MAKR
MARK
MASK
MKAS
MKSA
MSKA
MSKA
SAMK
SAKM
SKAM
SKMA
SMKA
Therefore, the 19th word in alphabetical order is "SAMK" (option C).

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Approach Solution -2

The word is MASK. The letters in alphabetical order are A, K, M, S.

We want to find the 19th word in the dictionary order.

1. Words starting with A:

There are 3! = 6 permutations starting with A.

The last word starting with A is ASMK (6th word).

2. Words starting with K:

There are 3! = 6 permutations starting with K.

The last word starting with K is KSMA (12th word).

3. Words starting with M:

There are 3! = 6 permutations starting with M.

The last word starting with M is MSKA (18th word).

Since we are looking for the 19th word, it must start with S.

4. Words starting with S:

The first word starting with S is SAKM.

The second word starting with S is SAMK.

So, the 19th word is SAMK.

Answer:

SAMK

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