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How many words are formed from the letters of the word EAMCET so that two vowels are never together?
- a)360
- b)114
- c)72
- d)54
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
How many words are formed from the letters of the word EAMCET so that ...
To solve this problem, we need to find the number of words that can be formed from the letters of the word "EAMCET" such that two vowels are never together.
First, let's determine the number of ways we can arrange the consonants. In the word "EAMCET", we have 3 consonants: M, C, and T. These can be arranged in 3! = 6 ways.
Next, let's consider the arrangement of the vowels A and E. Since we do not want two vowels to be together, we need to arrange them in such a way that there is at least one consonant between them.
To do this, we can treat the consonants M, C, and T as dividers. We can place the vowels in the spaces between these dividers.
There are 4 spaces between the consonants where the vowels can be placed: _M_C_T_.
To place the vowels, we need to choose 2 out of the 4 spaces. This can be done in C(4, 2) = 6 ways.
Now, let's consider the arrangement of the vowels themselves. Since we have 2 vowels (A and E), they can be arranged in 2! = 2 ways.
Therefore, the total number of words that can be formed from the letters of the word "EAMCET" such that two vowels are never together is 6 * 6 * 2 = 72.
Hence, the correct answer is option C) 72.
First, let's determine the number of ways we can arrange the consonants. In the word "EAMCET", we have 3 consonants: M, C, and T. These can be arranged in 3! = 6 ways.
Next, let's consider the arrangement of the vowels A and E. Since we do not want two vowels to be together, we need to arrange them in such a way that there is at least one consonant between them.
To do this, we can treat the consonants M, C, and T as dividers. We can place the vowels in the spaces between these dividers.
There are 4 spaces between the consonants where the vowels can be placed: _M_C_T_.
To place the vowels, we need to choose 2 out of the 4 spaces. This can be done in C(4, 2) = 6 ways.
Now, let's consider the arrangement of the vowels themselves. Since we have 2 vowels (A and E), they can be arranged in 2! = 2 ways.
Therefore, the total number of words that can be formed from the letters of the word "EAMCET" such that two vowels are never together is 6 * 6 * 2 = 72.
Hence, the correct answer is option C) 72.
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How many words are formed from the letters of the word EAMCET so that two vowels are never together?a)360b)114c)72d)54Correct answer is option 'C'. Can you explain this answer?
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How many words are formed from the letters of the word EAMCET so that two vowels are never together?a)360b)114c)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 How many words are formed from the letters of the word EAMCET so that two vowels are never together?a)360b)114c)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 How many words are formed from the letters of the word EAMCET so that two vowels are never together?a)360b)114c)72d)54Correct answer is option 'C'. Can you explain this answer?.
How many words are formed from the letters of the word EAMCET so that two vowels are never together?a)360b)114c)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 How many words are formed from the letters of the word EAMCET so that two vowels are never together?a)360b)114c)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 How many words are formed from the letters of the word EAMCET so that two vowels are never together?a)360b)114c)72d)54Correct answer is option 'C'. Can you explain this answer?.
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