Question

If the letters of the word ‘MOTHER’ be permuted among themselves and the words so formed are arranged as in a dictionary, what is the rank of the word ‘MOTHER’?

Answer 1

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.