Permutations and Combinations
Dictionary Words
IIT-JEE 2007
Grade 11

Question:

The letters of the word COCHIN are permuted and all permutations are arranged in alphabetical order. The number of words that appear before the word COCHIN is:
(1) $96$
(2) $48$
(3) $192$
(4) $360$

Step-by-Step Solution

Key Concept: Letters of COCHIN sorted: C,C,H,I,N,O. Words before COCHIN must start with C (no letter precedes C in the set). For the 2nd letter, letters $<$ O from the remaining $\{C,H,I,N,O\}$ are C,H,I,N — each gives $4! = 24$ words. Total $= 4 \times 24 = 96$.
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Correct Answer: (1)

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