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


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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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