The letters of the word ‘FATHER’ are taken and permuted in all possible ways. The words thus formed are arranged as in a dictionary and ranked. Then the rank of the given word is

Alphabetical order : AEFHRTTo find the rank of the word FATHER The number of words :        starting with A           = 5!       ''        ''  E           = 5!       ''        ''  FAE      = 3!       ''        ''  FAH      = 3!       ''        ''  FAR      = 3!       ''        ''  FATE    = 2!The next word in dictionary order is FATHERAEFHRTFATHER  = 2x(5!)+ 3x(3!) + 1x(2!)+1=261 Then the rank of the given word is 261