IIT JEE , AIEEE Forum - Mathematics , Algebra - permutation-Please explain clearly.

rahulraj1

The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in an English dictionary.What the number of words that appear before the word COCHIN ?

santosh05

hey here it involves concept n patience....
its a 6 letter word.......u hav to select a letter first which sud cum first in alphabatic order.....here its C
now keepin C constant find no of words dat can b formd,,,....its 5!
den u hav to analyse oder letters in order-------H den I N and O
den see no of words startin wid CC,CH,CI,CN ,co(4!)
u hav to preceed in dis way orderly till u get d desired word

Decoder

keep C_ _ _ _ _ ...
next early appearing letter is C again..

so it gets CC_ _ _ _ permutations possible -- 4!..
similarly CH _ _ _ _ -4! ways again..
now CI _ _ _ _ 4! ways again..
now CN _ _ _ _ 4! ways again..
now COCHIN...u get as the next letter..

so total permutations r - 4 (4!) = 96..

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