The letters of the word COCHIN are permuted a | vedclass

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(A) The letters of the word $COCHIN$ are $C, C, H, I, N, O$. Arranging them in alphabetical order, we get $C, C, H, I, N, O$.To find the number of wor

Vedclass · Accepted Answer

$96$

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(A) The letters of the word $COCHIN$ are $C, C, H, I, N, O$. Arranging them in alphabetical order, we get $C, C, H, I, N, O$.To find the number of words appearing before $COCHIN$, we consider words starting with letters that come before the letters in $COCHIN$ at each position.$1$. Words starting with $C$ (at the first position): The remaining letters are $C, H, I, N, O$. Since there are two $C$s,the number of arrangements is $\frac{5!}{2!} = \frac{120}{2} = 60$.$2$. However, we need words before $COCHIN$. Let's fix the first letter as $C$:- Words starting with $CC$: Remaining letters are $H, I, N, O$. Number of arrangements $= 4! = 24$.- Words starting with $CH$: Remaining letters are $C, I, N, O$. Number of arrangements $= 4! = 24$.- Words starting with $CI$: Remaining letters are $C, H, N, O$. Number of arrangements $= 4! = 24$.- Words starting with $CN$: Remaining letters are $C, H, I, O$. Number of arrangements $= 4! = 24$.- The next words start with $CO$. The first word starting with $CO$ is $COCHIN$.Total words before $COCHIN = 24 + 24 + 24 + 24 = 96$.

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

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