The letters, arranged alphabetically, are
E, H, M, O, R, T
Number of words beginning with E 5! = 120
Number of words beginning with H 5! = 120
Number of words beginning with ME 4! = 24
Number of words beginning with MH 4! = 24
Number of words beginning with MOE 3! = 6
Number of words beginning with MOH 3! = 6
Number of words beginning with MOR 3! = 6
Number of words beginning with MOTE 2! = 2
Number of words beginning with MOTHER 1
Total = 309
The position (rank) of the word ‘MOTHER’ is 309.