If all the words (with or without meaning) having five letters, formed using the letters o…

Question

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:

Accepted Answer

Letters of SMALL in alphabetical order: A, L, L, M, S (L repeated).

Words starting with A: $\dfrac{4!}{2!}=12$

Words starting with L: $4!=24$ (cumulative $36$)

Words starting with M: $\dfrac{4!}{2!}=12$ (cumulative $48$)

Words starting with SA: $\dfrac{3!}{2!}=3$ (cumulative $51$)

Words starting with SL: $3!=6$ (cumulative $57$)

Words starting with SMALL itself: this is the next word, position $58$.

$$\text{Rank} = 58$$

Solutions · 1