JEE Exam > JEE Questions > In how many different ways can the letters of...
Start Learning for Free
In how many different ways can the letters of the word 'GEOGRAPHY' be arranged such that the vowels must always come together?
- a)2520
- b)2530
- c)15130
- d)15120
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In how many different ways can the letters of the word GEOGRAPHY be ar...
Given:
The given number is 'GEOGRAPHY'
Calculation:
The word 'GEOGRAPHY' has 9 letters. It has the vowels E, O, A in it, and these 3 vowels must always come together. Hence these 3 vowels can be grouped and considered as a single letter. That is, GGRPHY(EOA).
Let 7 letters in this word but in these 7 letters, 'G' occurs 2 times, but the rest of the letters are different.
Now,
The number of ways to arrange these letters = 7!/2!
⇒ 7 × 6 × 5 × 4 × 3 = 2520
In the 3 vowels(EOA), all vowels are different
The number of ways to arrange these vowels = 3!
⇒ 3 × 2 × 1 = 6
Now,
The required number of ways = 2520 × 6
⇒ 15120
∴ The required number of ways is 15120.
Most Upvoted Answer
In how many different ways can the letters of the word GEOGRAPHY be ar...
To solve this problem, we need to consider the vowels (E, O, A) as a single entity. Therefore, the arrangement will be G-R-P-H-Y-V-E-O-A. Now, let's calculate the number of ways we can arrange these letters.
Step 1: Consider the arrangement of the consonants (G, R, P, H, Y).
Since there are 5 consonants, the number of ways to arrange them is 5! = 120.
Step 2: Consider the arrangement of the vowels (EOA).
Since there are 3 vowels, the number of ways to arrange them is 3! = 6.
Step 3: Consider the arrangement of the consonants and vowels together.
Since the vowels are treated as a single entity, we have 2 entities to arrange: (G-R-P-H-Y) and (EOA).
The number of ways to arrange these 2 entities is 2!.
Step 4: Multiply the results from Step 1, Step 2, and Step 3 to get the total number of arrangements.
Total number of arrangements = 5! * 3! * 2! = 120 * 6 * 2 = 1440.
However, we need to consider that the vowels (EOA) can also be arranged among themselves. Since there are 3 vowels, the number of ways to arrange them is 3!.
Step 5: Multiply the result from Step 4 with the number of ways to arrange the vowels.
Total number of arrangements = 1440 * 3! = 1440 * 6 = 8640.
Therefore, the correct answer is option D, 8640.
Step 1: Consider the arrangement of the consonants (G, R, P, H, Y).
Since there are 5 consonants, the number of ways to arrange them is 5! = 120.
Step 2: Consider the arrangement of the vowels (EOA).
Since there are 3 vowels, the number of ways to arrange them is 3! = 6.
Step 3: Consider the arrangement of the consonants and vowels together.
Since the vowels are treated as a single entity, we have 2 entities to arrange: (G-R-P-H-Y) and (EOA).
The number of ways to arrange these 2 entities is 2!.
Step 4: Multiply the results from Step 1, Step 2, and Step 3 to get the total number of arrangements.
Total number of arrangements = 5! * 3! * 2! = 120 * 6 * 2 = 1440.
However, we need to consider that the vowels (EOA) can also be arranged among themselves. Since there are 3 vowels, the number of ways to arrange them is 3!.
Step 5: Multiply the result from Step 4 with the number of ways to arrange the vowels.
Total number of arrangements = 1440 * 3! = 1440 * 6 = 8640.
Therefore, the correct answer is option D, 8640.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer?
Question Description
In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer?.
In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer?.
Solutions for In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In how many different ways can the letters of the word GEOGRAPHY be arranged such that the vowels must always come together?a)2520b)2530c)15130d)15120Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup