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

Step-by-step solution

Number of such words without both R together = total possible words - total possible words with both R together Number of such words start with A = 5 ! 2 ! - 4 ! = 36 Number of such words start with E = 5 ! 2 ! - 4 ! = 36 Number of such words start with FAE = 3 ! 2 ! - 2 = 1 Number of such words start with FAM = 3 ! 2 ! - 2 = 1 Number of such words start with FARE = 2 ! = 2 Number of such words start with FARMER = 1 Total = 77