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Permutation: Dictionary Order of CHCJL

XAT 2010 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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If all letters of the word "CHCJL" be arranged in an English dictionary, what will be the 50th50^{\text{th}} word?

  1. A.

    HCCLJ

  2. B.

    LCCHJ

  3. C.

    LCCJH

  4. D.

    JHCLC

  5. E.

    None of the above

Answer

C

Explanation

Alphabetical order of letters: C, C, H, J, L.

  • Words starting with C: remaining C, H, J, L   ⟹  4!=24\implies 4! = 24 words.
  • Words starting with H: remaining C, C, J, L   ⟹  4!2!=12\implies \frac{4!}{2!} = 12 words.
  • Words starting with J: remaining C, C, H, L   ⟹  4!2!=12\implies \frac{4!}{2!} = 12 words. Total words so far = 24+12+12=4824 + 12 + 12 = 48 words. 49th49^{\text{th}} word (starts with L): LCCHJ. 50th50^{\text{th}} word: LCCJH.

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