The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary.The number of words that appear before the word COCHIN is
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number of words start with A are 5! (if we fix first position as A then remaining 5 position can be arranged as 5!)
similarly with B also there are 5!..total--- 2×5!
then word start with CA_ _ _ _ this can be arranged as 4! similarly for CB, CC,CD,CE,CF,CG,CH....CN there are 13 possiblities to have O before C so there are 14×4!
then COA_ _ _ (3!),COB _ _ _ (3!) total -- 2× 3!
COCA_ _ (2!),COCB_ _(2!),COCC_ _ (2!), COCD_ _ (2!),COCE_ _ (2!),COCF _ _ (2!), COCG _ _ (2!) total--- 7×2!
then COCHA_(1!),COCHB_(1!),.....there are 9 possible arrangements before COCHI_. so 9×1!.
COCHIA,COCHIB.....COCHIM there 13 possible arrangements before the words COCHIN.
so total no.of words before Cochin are --(2×5!+4×14!+2×3!+7×2!+9×1!+13) if you calculate this you'll get no of words before the word Cochin.
hope it helps
similarly with B also there are 5!..total--- 2×5!
then word start with CA_ _ _ _ this can be arranged as 4! similarly for CB, CC,CD,CE,CF,CG,CH....CN there are 13 possiblities to have O before C so there are 14×4!
then COA_ _ _ (3!),COB _ _ _ (3!) total -- 2× 3!
COCA_ _ (2!),COCB_ _(2!),COCC_ _ (2!), COCD_ _ (2!),COCE_ _ (2!),COCF _ _ (2!), COCG _ _ (2!) total--- 7×2!
then COCHA_(1!),COCHB_(1!),.....there are 9 possible arrangements before COCHI_. so 9×1!.
COCHIA,COCHIB.....COCHIM there 13 possible arrangements before the words COCHIN.
so total no.of words before Cochin are --(2×5!+4×14!+2×3!+7×2!+9×1!+13) if you calculate this you'll get no of words before the word Cochin.
hope it helps
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