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In how many different ways can the letters of the word CORPORATION be arranged that the vowels always come together?
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In how many different ways can the letters of the word CORPORATION be ...
Arranging the letters of the word CORPORATION with vowels together
When we say that the vowels must always come together, we are essentially treating the group of vowels (O, O, A, I, O) as a single letter. This means we have to arrange 8 letters instead of 11.
Step 1: Identify the number of ways to arrange the vowels
Since we are treating the vowels as a single letter, we only have to arrange 8 letters instead of 11. Out of these 8 letters, the group of vowels (OOAIO) takes up 5 spots. Therefore, we have to arrange 3 consonants and the group of vowels in a line.
The number of ways to arrange 3 consonants in a line is 3! = 6.
Now, we have to arrange the group of vowels (OOAIO) in a line. Since there are 5 letters in the group, the number of ways to arrange them is 5! = 120.
Step 2: Combine the arrangements
Now that we have the number of ways to arrange the consonants and the vowels, we can combine the arrangements to get the final answer.
Since the arrangement of the consonants and the vowels are independent of each other, we can use the multiplication principle to find the total number of arrangements.
Therefore, the total number of arrangements = 6 x 120 = 720.
Final answer
There are 720 different ways to arrange the letters of the word CORPORATION such that the vowels always come together.
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In how many different ways can the letters of the word CORPORATION be arranged that the vowels always come together?
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In how many different ways can the letters of the word CORPORATION be arranged that the vowels always come together? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In how many different ways can the letters of the word CORPORATION be arranged that the vowels always come together? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word CORPORATION be arranged that the vowels always come together?.
In how many different ways can the letters of the word CORPORATION be arranged that the vowels always come together? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In how many different ways can the letters of the word CORPORATION be arranged that the vowels always come together? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word CORPORATION be arranged that the vowels always come together?.
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