Permutations and Combinations 3 Question 7
7. 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
(2007, 3M)
(a) 360
(b) 192
(c) 96
(d) 48
Numerical Value
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Answer:
Correct Answer: 7. (c)
Solution:
- Arrange the letters of the word COCHIN as in the order of dictionary CCHINO.
Consider the words starting from $C$.
There are 5! such words. Number of words with the two C’s occupying first and second place $=4$ !.
Number of words starting with $CH, CI, CN$ is 4 ! each.
Similarly, number of words before the first word starting with $CO=4 !+4 !+4 !+4 !=96$.
The word starting with $CO$ found first in the dictionary is COCHIN. There are 96 words before COCHIN.
