Question

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

• A. $360$
• B. $192$
• C. $96$
• D. $48$

Answer 1

The correct option is C

$96$

Finding the number of words :

The given word is COCHIN

So, we have two times $C$ appearing in the word.

Fixing position these $C$ we have number of letters for permutation $=4$

Therefore, the number of words, having two letter of $C$ in first and second places $=4!$

Similarly,

The number of words starting with letter $CH$$=4!$

The number of words starting with letter $CI$ $=4!$

The number of words starting with letter $CN$ $=4!$

Therefore,

The total number of words that appear before the word ‘COCHIN’

$$\begin{gathered} =4!+4!+4!+4! \\ =\left(4\times 3\times 2\times 1\right)+\left(4\times 3\times 2\times 1\right)+\left(4\times 3\times 2\times 1\right)+\left(4\times 3\times 2\times 1\right) \\ =24+24+24+24 \\ =96 \end{gathered}$$

Hence, option (C) is the correct answer.