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JEE Main 20163 April
Exam
JEE Main
Year
2016
Date
3 April
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2016 · 3 April · Mathematics · Permutation and Combination

If all the words (with or without meaning) having five letters,...

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALLSMALL and arranged as in a dictionary; then the position of the word SMALLSMALL is

Options

  1. A52nd{52}^{nd}
  2. B58th{58}^{th}
  3. C46th{46}^{th}
  4. D59th{59}^{th}

Correct answer

B. 58th{58}^{th}

Step-by-step solution

SMALLSMALL
Total number of words formed would be 5!2!=60\dfrac{5!}{2!} = 60
When arranged as per dictionary. The words starting from AA

A−−−−4!2!=12A - - - - \dfrac{4!}{2!} = 12

The words starting from LL

L−−−−=4!=24L - - - - = 4! = 24

The words starting from MM

M−−−−=4!2!=12M - - - - = \dfrac{4!}{2!} = 12

The words starting from SS

SA−−−=3!2!=3SA - - - = \dfrac{3!}{2!} = 3

SL−−−3!=6SL - - - 3! = 6
SMALL=1SMALL = 1
∴∴ Rank would be 12+24+12+3+6+1=5812 + 24 + 12 + 3 + 6 + 1 = 58
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