If-the-permutations-of-a-b-c-d-e-taken-all-together-be-written-down-in-alphabetical-order-as-in-dictionary-and-numbered-then-the-rank-of-the-permutation-debac-is-

Question Number 42093 by amansingh@123 last updated on 17/Aug/18

If the permutations of a, b, c, d, e taken

all together be written down in

alphabetical order as in dictionary

and numbered, then the rank of the

permutation d e b a c is

Answered by $@ty@m last updated on 17/Aug/18

N o . o f p e r m . o f l e t t e r s b e g i n n i n g w i t h a = 4! = 24

N o . o f p e r m . o f l e t t e r s b e g i n n i n g w i t h b = 4! = 24

N o . o f p e r m . o f l e t t e r s b e g i n n i n g w i t h c = 4! = 24

N o . o f p e r m . o f l e t t e r s b e g i n n i n g w i t h d a = 3! = 6

N o . o f p e r m . o f l e t t e r s b e g i n n i n g w i t h d b = 3! = 6

N o . o f p e r m . o f l e t t e r s b e g i n n i n g w i t h d c = 3! = 6

N o . o f p e r m . o f l e t t e r s b e g i n n i n g w i t h d e a = 2! = 2

∴ t h e r a n k o f t h e p e r m . d e b a c =

24 \times 3 + 6 \times 3 + 2 + 1 = 93

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