if all the words with or without meaning five letters are arranged using the letters of the word SMALL as in dictionary, then the position of the word SMALL, is

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$58^{th}$

$46^{th}$

$52^{th}$

$59^{th}$

answer is D.

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Detailed Solution

We find that

Number of words beginning with $A = \frac{4!}{2!} = 12$

Number of words beginning with $L = 4! = 24$

Number of words beginning with $M = \frac{4!}{2!} = 12$

The word SMALL is in the series of words beginning with S.

Number of words beginning with $S A = \frac{3!}{2!} = 3$

Number of words beginning with $S L = 3! = 6$

Number of words beginning with $S M = \frac{3!}{2!} = 3$

One of these words is the word SMALL. Number of words beginning with SMA=1

The word beginning with SMA is SMALL. Hence, the position of the word SMALL is

$(12 + 24 + 12 + 3 + 6 + 1)^{th} = 58^{th}$

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