Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the letters of the word ACTIVE are arranged in all possible ways and the words are arranged in a dictionary, then find the rank of the word ACTIVE.  <s

If the letters of the word ACTIVE are arranged in all possible ways and the words are arranged in a dictionary, then find the rank of the word ACTIVE.

 

Option: 1

92


Option: 2

16


Option: 3

56


Option: 4

38


Answers (1)

best_answer

Given that the word is ACTIVE. 

The lexicographic order of the letters of the given word is A, C, E, I, T, V. The words that begin with A will come first in the lexicographic order.

If the letter A is in the first place of the six-letter word, then the remaining four letters can be arranged in 3! ways. On proceeding like this,

\begin{aligned} & \operatorname{ACE}(---)=3 ! \text { ways } \\ & \operatorname{ACI}(---)=3 ! \text { ways } \\ & \operatorname{ACTE}(--)=2 ! \text { ways } \\ & \operatorname{ACTIE}(-)\:\: =1 \text { ! ways } \\ & \operatorname{ACTIVE}\: \: \: \: \: =0 \text { ! ways } \end{aligned}

So, the rank of the word ACTIVE is given by,

\begin{aligned} & =3 !+3 !+2 !+1 !+0 ! \\ & =(3 \times 2 \times 1)+(3 \times 2 \times 1)+(2 \times 1)+1+1 \\ & =6+6+2+1+1 \\ & =16 \end{aligned}

Therefore, the rank of the word ACTIVE is 16

Posted by

shivangi.bhatnagar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: NIT Patna cut-offs for engineering programmes; know closing ranks for BTech admission
anam-khan

JEE Main 2025: Why IIT Bombay CSE remains top priority of toppers; cut-offs of last 7 years
anam-khan

JEE Main 2025: NIT cut-off marks for BTech in AI and ML, data science engineering

Latest Question