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 LUCKY are arranged in all possible ways and the words are arranged in a dictionary, then find the rank of the word LUCKY.  <str

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

 

Option: 1

92


Option: 2

61


Option: 3

93


Option: 4

95


Answers (1)

best_answer

Given that the word is LUCKY. 

The lexicographic order of the letters of the given word is C, K, L, U, Y. The words that begin with C will come first in the lexicographic order.

If the letter C is in the first place of the five-letter word, then the remaining four letters can be arranged in 4! ways. On proceeding like this, 

\begin{aligned} & \mathrm{C}(----)=4 ! \text { ways } \\ & \mathrm{K}(----)=4 ! \text { ways } \\ & \mathrm{LC}(---)=3 ! \text { ways } \\ & \mathrm{LK}(---)=3 ! \text { ways } \\ & \mathrm{LUCKY}=0 \text { ! ways } \end{aligned}

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

\begin{aligned} & =4 !+4 !+3 !+3 !+0 ! \\ & =(4 \times 3 \times 2 \times 1)+(4 \times 3 \times 2 \times 1)+(3 \times 2 \times 1)+(3 \times 2 \times 1)+1 \\ & =24+24+6+6+1 \\ & =61 \end{aligned}

Therefore, the rank of the word LUCKY is  61

Posted by

Ritika Harsh

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 Rourkela cut-offs for CSE, chemical engineering drop; last years' closing ranks
anam-khan

JEE Main 2025 Live: NTA exam city slip at jeemain.nta.nic.in soon; session 1 schedule
anam-khan

JEE Main 2025 schedule out for session 1; paper 1 from January 22

Latest Question