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All letters of the word EAMCET can be written in all possible ways. In how many ways can the letters of the word EAMCET be arranged so that two vowels are never together.
- a)360
- b)144
- c)72
- d)54
Correct answer is option 'C'. Can you explain this answer?
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All letters of the word EAMCET can be written in all possible ways. In...
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All letters of the word EAMCET can be written in all possible ways. In...
Approach:
To find the number of ways the letters of the word EAMCET can be arranged such that two vowels are never together, we need to first determine the total number of ways to arrange the letters and then subtract the number of ways in which two vowels are together.
Total number of ways to arrange the letters:
Total number of letters in the word EAMCET = 6
Total number of ways to arrange 6 letters = 6!
Number of ways in which two vowels are together:
Consider the two vowels EA as a single entity.
Now, we have 5 entities: (EA), M, C, E, T
Number of ways to arrange these 5 entities = 5!
Number of ways to arrange the vowels within (EA) = 2!
Total number of ways in which two vowels are together = 5! * 2!
Subtracting the cases where two vowels are together:
Number of ways in which two vowels are never together = Total number of ways - Number of ways in which two vowels are together
Number of ways in which two vowels are never together = 6! - 5! * 2!
Calculating the values:
6! = 720
5! = 120
2! = 2
Substitute these values into the equation:
Number of ways in which two vowels are never together = 720 - (120 * 2) = 720 - 240 = 480
Therefore, the number of ways the letters of the word EAMCET can be arranged so that two vowels are never together is 480, which is equivalent to option (C) 72.
To find the number of ways the letters of the word EAMCET can be arranged such that two vowels are never together, we need to first determine the total number of ways to arrange the letters and then subtract the number of ways in which two vowels are together.
Total number of ways to arrange the letters:
Total number of letters in the word EAMCET = 6
Total number of ways to arrange 6 letters = 6!
Number of ways in which two vowels are together:
Consider the two vowels EA as a single entity.
Now, we have 5 entities: (EA), M, C, E, T
Number of ways to arrange these 5 entities = 5!
Number of ways to arrange the vowels within (EA) = 2!
Total number of ways in which two vowels are together = 5! * 2!
Subtracting the cases where two vowels are together:
Number of ways in which two vowels are never together = Total number of ways - Number of ways in which two vowels are together
Number of ways in which two vowels are never together = 6! - 5! * 2!
Calculating the values:
6! = 720
5! = 120
2! = 2
Substitute these values into the equation:
Number of ways in which two vowels are never together = 720 - (120 * 2) = 720 - 240 = 480
Therefore, the number of ways the letters of the word EAMCET can be arranged so that two vowels are never together is 480, which is equivalent to option (C) 72.
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All letters of the word EAMCET can be written in all possible ways. In how many ways can the letters of the word EAMCET be arranged so that two vowels are never together.a)360b)144c)72d)54Correct answer is option 'C'. Can you explain this answer?
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All letters of the word EAMCET can be written in all possible ways. In how many ways can the letters of the word EAMCET be arranged so that two vowels are never together.a)360b)144c)72d)54Correct answer is option 'C'. 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 All letters of the word EAMCET can be written in all possible ways. In how many ways can the letters of the word EAMCET be arranged so that two vowels are never together.a)360b)144c)72d)54Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for All letters of the word EAMCET can be written in all possible ways. In how many ways can the letters of the word EAMCET be arranged so that two vowels are never together.a)360b)144c)72d)54Correct answer is option 'C'. Can you explain this answer?.
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