Q153 / 270 · NDA 2022 (Phase 2) · Mathematics

If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there in the list before the first word that starts with $C$ ?

  • A
    $302400$
  • B
    $403600$
  • Correct answer
    C
    $907200$
  • D
    $1814400$

Solution

Given word 'MATHEMATICS' No. of words start with $A=\frac{10!}{2!2!}$ $\therefore \quad$ No. of words before the first word that start with $c=\frac{10!}{2!2!}=907200$

Hence, the correct answer is option: 'C'.

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