All the arrangements, with or without meaning, of the word PARMER are written excluding any word that has two R appearing together. The arrangements are listed serially I the alphabetic order as in the English dictionary. Then the serial number of the word PARMER in this list is

PARMER no of words starting with A and (R’s not together) $=\frac{5!}{2!}-4!=36$

                          P, R, M E R           -    

Starting with E and R’s not together

                                          -

                                                        P, M, A, (RR) 

 $=\frac{5!}{2!}-4!=36$

Starting with PAE and R'S not together

                                                   -

$=\frac{3!}{2!}-2=1$

Starting with PAM and R’S not together

                          -

$=\frac{3!}{2!}-2=1$

Starting with PARE      =2!=2

Starting with PARMER=1

             Rank=36+36+1+1+2+1

                      =77