Permutations
Question
If the letters of the word MOTHER are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MOTHER is
Easy
Solution
The number of words starting from E are = 5 ! = 120
The number of words starting from H are = 5 != 120
The number of words starting from ME are = 4! = 24
The number of words starting from MH are = 4! =24
The number of words starting from MOE are = 3 ! = 6
The number of words starting from MOH are = 3!= 6
The number of words starting from MOR are = 3 ! = 6
The number of words starting from MOTE are = 2 != 2
The number of words starting from MOTHER are = 1!= 1
Hence, rank of the word MOTHER
=2 (120) + 2 (24) + 3 (6) + 2 + 1= 309
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