Permutations and Combinations 3 Question 6

6. If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is

(2016 Main)

(a) 46 th

(b) 59 th

(c) $52 nd$

(d) 58 th

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Answer:

Correct Answer: 6. (d)

Solution:

  1. Clearly, number of words start with $A=\frac{4 !}{2 !}=12$

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

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

Number of words start with $SA=\frac{3 !}{2 !}=3$

Number of words start with $SL=3 !=6$

Note that, next word will be “SMALL”.

Hence, the position of word “SMALL” is 58th.



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