CAT Exam > CAT Questions > In how many different ways can the letters o...
Start Learning for Free
In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?
- a)720
- b)1440
- c)5040
- d)3600
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
In how many different ways can the letters of the word ‘THERAPY’ be a...
Introduction:
In this problem, we are given the word 'THERAPY' and we need to find the number of different ways we can arrange its letters such that the vowels (E, A) never come together.
Approach:
To solve this problem, we can use the concept of permutations and combinations. We will calculate the total number of arrangements of all the letters and then subtract the number of arrangements where the vowels come together.
Step 1: Calculate the total number of arrangements:
The word 'THERAPY' has 7 letters. The number of ways we can arrange these 7 letters is given by 7!.
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
So, there are 5040 different ways to arrange the letters of the word 'THERAPY' without any restrictions.
Step 2: Calculate the number of arrangements where vowels come together:
To calculate the number of arrangements where the vowels (E, A) come together, we can consider them as a single unit. So, we have 6 units to arrange: T, H, R, P, Y, (EA).
The number of ways we can arrange these 6 units is given by 6!.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
However, within the (EA) unit, the vowels can be arranged in 2! = 2 ways.
So, the total number of arrangements where the vowels come together is 720 x 2 = 1440.
Step 3: Calculate the number of arrangements where vowels never come together:
To calculate the number of arrangements where the vowels never come together, we subtract the number of arrangements where the vowels come together from the total number of arrangements.
Number of arrangements where vowels never come together = Total number of arrangements - Number of arrangements where vowels come together
= 5040 - 1440
= 3600
Conclusion:
Therefore, the number of different ways we can arrange the letters of the word 'THERAPY' such that the vowels never come together is 3600.
In this problem, we are given the word 'THERAPY' and we need to find the number of different ways we can arrange its letters such that the vowels (E, A) never come together.
Approach:
To solve this problem, we can use the concept of permutations and combinations. We will calculate the total number of arrangements of all the letters and then subtract the number of arrangements where the vowels come together.
Step 1: Calculate the total number of arrangements:
The word 'THERAPY' has 7 letters. The number of ways we can arrange these 7 letters is given by 7!.
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
So, there are 5040 different ways to arrange the letters of the word 'THERAPY' without any restrictions.
Step 2: Calculate the number of arrangements where vowels come together:
To calculate the number of arrangements where the vowels (E, A) come together, we can consider them as a single unit. So, we have 6 units to arrange: T, H, R, P, Y, (EA).
The number of ways we can arrange these 6 units is given by 6!.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
However, within the (EA) unit, the vowels can be arranged in 2! = 2 ways.
So, the total number of arrangements where the vowels come together is 720 x 2 = 1440.
Step 3: Calculate the number of arrangements where vowels never come together:
To calculate the number of arrangements where the vowels never come together, we subtract the number of arrangements where the vowels come together from the total number of arrangements.
Number of arrangements where vowels never come together = Total number of arrangements - Number of arrangements where vowels come together
= 5040 - 1440
= 3600
Conclusion:
Therefore, the number of different ways we can arrange the letters of the word 'THERAPY' such that the vowels never come together is 3600.
Free Test
FREE
| Start Free Test |
Community Answer
In how many different ways can the letters of the word ‘THERAPY’ be a...
Total no. of cases = 7!
There are two vowels, E and A.
Considering them as one word, total number of possible words = 6!, and the two letters can be arranged among themselves in 2! Ways.
So, number of cases where vowels will be together = 6! × 2!
So, total no of ways when vowels never come together = 7!- (6! × 2!) = 3600
Hence, the correct option is (d).
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer?
Question Description
In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer?.
In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer?.
Solutions for In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct 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 ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct 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 ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct 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 ‘THERAPY’ be arranged so that the vowels never come together?a)720b)1440c)5040d)3600Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup