# If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac.

Given the letters a, b, c, d, and e.

Arranging the permutations of the letters a, b, c, d, and e in a dictionary:

To find: Rank of word debac in dictionary.

First comes, words starting from letter a = 4! = 24

words starting from letter b = 4! = 24

words starting from letter c = 4! = 24

words starting from letter d:

words starting from da = 3! = 6

words starting from db = 3! = 6

words starting from dc = 3! = 6

words starting from dea = 2! = 4

words starting from deb:

debac = 1

Rank of the word debac = 24 + 24 + 24 + 6 + 6 + 6 + 4 + 1

= 95

Hence the rank of the word debc in arranging the letters a, b, c, d, and e in a dictionary among its permutations is 95.

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