How to Find the Rank of a Word in Dictionary Without Repetition ?
For some students "Rank finding in dictionary problems" is a difficult topic in quantitative aptitude. Actually it is not like that. Once we understand the concept, it is not a difficult one to understand.
Question 1 :
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words (i) GARDEN (ii) DANGER.
Solution :
Let us write the given word with alphabetical order,
A, D, E, G, N, R
Number of words starting with the letter A by rearranging the letters of the given word "GARDEN"
A _ _ _ _ _ = 5!
Number of words starting with the letter D
D _ _ _ _ _ = 5!
Number of words starting with the letter E
E _ _ _ _ _ = 5!
Number of words starting with the letter GAD
GAD _ _ _ = 3!
Number of words starting with the letter GAE
GAE _ _ _ = 3!
Number of words starting with the letter GAN
GAN _ _ _ = 3!
Number of words starting with the letter GAR
GAR _ _ _ = 1
The remaining letters are in alphabetical order.
3(5!) + 3(3!) + 1 = 3(120) + 3(6) + 1
= 360 + 18 + 1
= 379
Hence the total number of ways are 379.
Let us write the given word with alphabetical order,
A, D, E, G, N, R
Number of words starting with the letter A by rearranging the letters of the given word "GARDEN"
A _ _ _ _ _ = 5!
Number of words starting with the letter DAE
D A E _ _ _ = 3!
Number of words starting with the letter DAG
D A G _ _ _ = 3!
Number of words starting with the letter DANE
D A N E _ _ = 2!
Number of words starting with the letter DANG
D A N G _ _ = 1
If we use the remaining letters in the alphabetical order.
5! + 2(3!) + 2! + 1 = 120 + 2(6) + 2 + 1
= 120 + 12 + 3
= 135
Hence the total number of ways are 135.
After having gone through the stuff given above, we hope that the students would have understood "How to Find the Rank of a Word in Dictionary Without Repetition".
Apart from the stuff given above, if you want to know more about "How to Find the Rank of a Word in Dictionary Without Repetition".
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Mar 28, 24 02:01 AM
Mar 26, 24 11:25 PM
Mar 26, 24 08:53 PM