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:
- 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.
