Question

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

• A. 360
• B. 192
• C. 96
• D. 48

Answer 1

The correct option is C 96

The letter of word COCHINin alphabetic order are C,C,H,I,N,O.
Fixing first letter C and keeping C at second place, rest 4 can be arranged in 4! ways.
Similarly the words starting with CH, CI, CN are 4!in each case.
Then fixing first two letters as CO next four places when filled in alphabetic order give the word COCHIN.
$\therefore$ Numbers of words coming before COCHIN are $4\times 4!=4\times 24=96$