if letters of word 'MOTHER' are written in all possible orders and these words are written out as in dictionary - Maths - Permutations and Combinations

Question

if letters of word 'MOTHER' are written in all possible orders
and these words are written out as in dictionary find the rank pof
the word 'MOTHER'

ramandeep.singh · Accepted Answer

The given word is MOTHER In a dictionary, the words are arranged
in alphabetical order The words beginning with E, H, M, O, R and T
are written in order
Number of words starting with E = 5! = 120
Number of words starting with H = 5! = 120
Number of words starting with M = 5! = 120, but one of these
words is MOTHER
Now, number of words with ME = 4! = 24
Number of words with MH = 4! = 24
Number of words with MO = 4! = 24, but one of these words is
MOTHER
Now, number of words with MOE = 3! = 6
Number of words with MOH = 3! = 6
Number of words with MOR = 3! = 6
Number of words with MOT = 3! = 6, but one of these words is
MOTHER
The first word beginning with MOT is MOTEHR The second word is
MOTERH The third word is MOTHER
Therefore, rank of MOTHER = 2(120) + 2(24) + 3(6) + 3
= 309

if letters of word 'MOTHER' are written in all possible orders and these words are written out as in dictionary find the rank pof the word 'MOTHER'.