Quant Exam > Quant 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 'MATHEMATICS' be arranged such that the vowels must always come together?
- a)9800
- b)100020
- c)120960
- d)140020
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In how many different ways can the letters of the word 'MATHEMATICS' b...
In the word 'MATHEMATICS', we'll consider all the vowels AEAI together as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice
Number of ways of arranging these letters =8! / ((2!)(2!))= 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters =4! / 2!= 12.
Required number of words = (10080 x 12) = 120960
Most Upvoted Answer
In how many different ways can the letters of the word 'MATHEMATICS' b...
Just see the multiple of 9 because when you try to find answer with the help of factorial than 9 is there when no. Multiples.
Free Test
FREE
| Start Free Test |
Community Answer
In how many different ways can the letters of the word 'MATHEMATICS' b...
To solve this problem, we need to first identify the vowels in the word 'MATHEMATICS'. The vowels in the word are A, E, A, I.
Now, let's consider the vowels as a single entity. So, we have 'MTHMTCS' and 'AEA'.
First, let's calculate the number of ways to arrange the consonants 'MTHMTCS'. There are 7 consonants in total, but 'T' and 'M' are repeated twice. Therefore, the number of ways to arrange the consonants is given by 7!/2! = 2520.
Next, let's consider the vowels 'AEA'. Since all three vowels are the same, we need to consider the number of ways to arrange them within themselves. This is given by 3!/2! = 3.
Now, we need to consider the arrangement of the consonants and vowels as a whole. Since we have treated the vowels as a single entity, we now have 2520 * 3 = 7560 ways to arrange the consonants and vowels together.
However, the vowels themselves can be arranged in 3! = 6 ways (since they are the same). Therefore, we need to multiply the previous result by 6 to account for the different arrangements of the vowels.
So, the final answer is 7560 * 6 = 45,360.
Therefore, the number of different ways the letters of the word 'MATHEMATICS' can be arranged such that the vowels always come together is 45,360.
The correct answer is option C) 120,960.
Now, let's consider the vowels as a single entity. So, we have 'MTHMTCS' and 'AEA'.
First, let's calculate the number of ways to arrange the consonants 'MTHMTCS'. There are 7 consonants in total, but 'T' and 'M' are repeated twice. Therefore, the number of ways to arrange the consonants is given by 7!/2! = 2520.
Next, let's consider the vowels 'AEA'. Since all three vowels are the same, we need to consider the number of ways to arrange them within themselves. This is given by 3!/2! = 3.
Now, we need to consider the arrangement of the consonants and vowels as a whole. Since we have treated the vowels as a single entity, we now have 2520 * 3 = 7560 ways to arrange the consonants and vowels together.
However, the vowels themselves can be arranged in 3! = 6 ways (since they are the same). Therefore, we need to multiply the previous result by 6 to account for the different arrangements of the vowels.
So, the final answer is 7560 * 6 = 45,360.
Therefore, the number of different ways the letters of the word 'MATHEMATICS' can be arranged such that the vowels always come together is 45,360.
The correct answer is option C) 120,960.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer?
Question Description
In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer?.
In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer?.
Solutions for In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. 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 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. 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 'MATHEMATICS' be arranged such that the vowels must always come together?a)9800b)100020c)120960d)140020Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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
|
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