If all the letters of the word ‘REPEAT’ are permuted in all possible ways and if the six letter permutations thus formed are arranged in the dictionary order, then the rank of the word REPEAT is

Alphabetical order of REPEAT

      A, E, E, P, R, T

No of words begin with A = $\frac{5!}{2!}=60$

No of words begin with E = 5!=120

No of words begin with P = $\frac{5!}{2!}=60$

No of words begin with RA = $\frac{4!}{2!}=12$

                                      RE A = 3!

                                      RE E = 3!           

                                    REPA = 2!

                              REPEAR = 1

Rank = 60+120+60+12+3!+3!+2!+1

           = 267