If the letters of the word COCHIN are rearran | vedclass

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(C) The letters of the word $COCHIN$ are $\{C, C, H, I, N, O\}$.Total number of permutations = $\frac{6!}{2!} = \frac{720}{2} = 360$.To find the numbe

Vedclass · Accepted Answer

$96$

Vedclass · Answer

(C) The letters of the word $COCHIN$ are $\{C, C, H, I, N, O\}$.Total number of permutations = $\frac{6!}{2!} = \frac{720}{2} = 360$.To find the number of words before $COCHIN$,we arrange the letters in alphabetical order: $C, C, H, I, N, O$.$1$. Words starting with $C$ (followed by $C$): The remaining letters are $\{H, I, N, O\}$. Number of words = $4! = 24$.$2$. Words starting with $CH$: The remaining letters are $\{C, I, N, O\}$. Number of words = $4! = 24$.$3$. Words starting with $CI$: The remaining letters are $\{C, H, N, O\}$. Number of words = $4! = 24$.$4$. Words starting with $CN$: The remaining letters are $\{C, H, I, O\}$. Number of words = $4! = 24$.Total words before $COCHIN$ = $24 + 24 + 24 + 24 = 96$.

If the letters of the word $COCHIN$ are rearranged and all permutations are arranged in alphabetical order as in an English dictionary,how many words appear before the word $COCHIN$?

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