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 :
96
Solution :
The letter of word $$COCHIN$$ in 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 $$COCHIN.$$
∴ Numbers of words coming before $$COCHIN$$ are
\[4 \times 4! = 4 \times 24 = 96\]
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
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