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EEJ MAIN Mathematics QUESTION #6932
Question 1

All five-letter words (meaningful or not) are formed using the letters of the word SMALL and listed in alphabetical (dictionary) order. What is the position of the word SMALL in this list?

  • 59th
  • 52nd
  • 58th✔️
  • 46th
Correct Answer Explanation

Letters in SMALL: A, L, L, M, S (sorted: A, L, L, M, S). Note L repeats twice.

Words starting with A: remaining letters M, L, L, S — arrangements $= \frac{4!}{2!} = 12$

Words starting with L: remaining A, L, M, S — arrangements $= 4! = 24$

Words starting with M: remaining A, L, L, S — arrangements $= \frac{4!}{2!} = 12$

Words starting with SA: remaining L, L, M — arrangements $= \frac{3!}{2!} = 3$

Words starting with SL: remaining A, L, M — arrangements $= 3! = 6$

Words starting with SM: next is SMA... then SMALL itself.

Words starting with SMA: remaining L, L — arrangements $= \frac{2!}{2!} = 1$ (i.e., SMALL itself is next after SMAAL... )

Total before SMALL: $12+24+12+3+6=57$, so SMALL is at position $\mathbf{58}$.