Question

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

(a) 48 

(b) 96 

(c) 192 

(d) 360

Answer 1

(b) 96

To determine the rank of the word COCHIN when the letters of the word ‘COCHIN’ are permuted and all permutations arranged in alphabetical order, we see that all words begin with C. So we have the following cases when permuted words are in alphabetical. 

I. First two letters are CC 

Then the number of ways of arranging the remaining 4 letters 0, H, I, N in remaining 4 places 4 ! 

∴ Number of word having CC has first two letters = 24 

II. First two letters are CH (next to CC in alphabetical order) 

Here also, as in case I, 

Number of words with CH as first two letters = 4 ! = 24 

Similarly, the number of words with CI and CN as their first two letters will be 24 each. 

The first word with CO as first two letters is COCHIN 

∴ 24 + 24 + 24 + 24 = 96 words appear before COCHIN.