All the letters of the word ANIMAL are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word ANIMAL is \(x\), then the permutation with rank \(x\), among the permutations obtained by permuting the letters of the word PERSON and arranging the permutations thus formed in dictionary order is

• A

  ENOPRS
• B

  NOSPRE
• C

  NOEPRS
• Correct answer
  D

  ESORNP

Solution

If we arrange the letter of word ANIMAL in alphabetic order then, we get AAILMN, now to find the rank of word ANIMAL, \(x\) (given) \(\begin{aligned} & \text { AA ......... 4! } \\ & \text { AI ......... 4! } \\ & \text { AL ......... 4! } \\ & \text { AM ......... 4! } \\ & \text { ANA ......... 3! } \\ & \text { ANIA ......... 2! } \\ & \text { ANIL .......... 2! } \\ & \text { ANIMAL ......... } 1 \\ & 107=x \\ \end{aligned}\) Now, similarly for word PERSON, if we arrange the letters in alphabetic order, we get ENOPRS, now to find the word having 107 ways ,
So, ESORNP is required word. Hence, option (4) is correct.

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