Question

If all the letters of the word 'QUEST' are arranged in all possible ways and put in dictionary order, then find the rank of the given word.

Answer 1

Number of words beginning with${=}^4{\text{P}}_4=24$
Number of words beginning with $QE{=}^3{\text{P}}_3=6$
Number ofwords beginning with $QS=6$
Number of words beginning with $QT=6.$
Next word is 'QUEST'
its rank is $24+6+6+6+1=43.$