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In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
- a)47200
- b)48000
- c)42000
- d)50400
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In how many different ways can the letters of the word 'CORPORATION' b...
Vowels in the word "CORPORATION" are O,O,A,I,O
Lets make it as CRPRTN(OOAIO)
This has 7 lettes, where R is twice so value = 7!/2!
= 2520
Vowel O is 3 times, so vowels can be arranged = 5!/3!
= 20
Total number of words = 2520 * 20 = 50400
Most Upvoted Answer
In how many different ways can the letters of the word 'CORPORATION' b...
Problem:
In how many different ways can the letters of the word CORPORATION be arranged so that the vowels always come together?
Solution:
To solve this problem, we need to consider the vowels (O, O, A, I, O) as a single entity. Let's call this entity "X". Therefore, we have the following arrangement:
R, P, R, T, N, X, C, N
Now, we can treat "X" as a single letter and find the number of ways to arrange the letters.
Step 1: Count the total number of letters
The word CORPORATION has 11 letters, including the repeated letters (O, O). So, we have a total of 11 letters.
Step 2: Count the number of ways to arrange the vowels
Since the vowels (O, O, A, I, O) are treated as a single entity (X), the number of ways to arrange the vowels is 5!.
Step 3: Count the number of ways to arrange the remaining letters
After treating the vowels as a single entity, we have a total of 7 letters (R, P, R, T, N, X, C, N). Among these, R and N are repeated twice. So, the number of ways to arrange the remaining letters is 7! / (2! * 2!).
Step 4: Calculate the total number of arrangements
To get the total number of arrangements, we need to multiply the number of ways to arrange the vowels with the number of ways to arrange the remaining letters.
Total number of arrangements = (5!) * (7! / (2! * 2!))
Simplifying this expression:
(5!) * (7! / (2! * 2!)) = (5!) * (7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 5! * 7 * 6 * 5 * 4 * 3
Step 5: Calculate the final answer
Evaluate the expression 5! * 7 * 6 * 5 * 4 * 3 to get the final answer.
5! = 5 * 4 * 3 * 2 * 1 = 120
Final answer = 120 * 7 * 6 * 5 * 4 * 3 = 50400
Therefore, the correct answer is option D) 50400.
In how many different ways can the letters of the word CORPORATION be arranged so that the vowels always come together?
Solution:
To solve this problem, we need to consider the vowels (O, O, A, I, O) as a single entity. Let's call this entity "X". Therefore, we have the following arrangement:
R, P, R, T, N, X, C, N
Now, we can treat "X" as a single letter and find the number of ways to arrange the letters.
Step 1: Count the total number of letters
The word CORPORATION has 11 letters, including the repeated letters (O, O). So, we have a total of 11 letters.
Step 2: Count the number of ways to arrange the vowels
Since the vowels (O, O, A, I, O) are treated as a single entity (X), the number of ways to arrange the vowels is 5!.
Step 3: Count the number of ways to arrange the remaining letters
After treating the vowels as a single entity, we have a total of 7 letters (R, P, R, T, N, X, C, N). Among these, R and N are repeated twice. So, the number of ways to arrange the remaining letters is 7! / (2! * 2!).
Step 4: Calculate the total number of arrangements
To get the total number of arrangements, we need to multiply the number of ways to arrange the vowels with the number of ways to arrange the remaining letters.
Total number of arrangements = (5!) * (7! / (2! * 2!))
Simplifying this expression:
(5!) * (7! / (2! * 2!)) = (5!) * (7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 5! * 7 * 6 * 5 * 4 * 3
Step 5: Calculate the final answer
Evaluate the expression 5! * 7 * 6 * 5 * 4 * 3 to get the final answer.
5! = 5 * 4 * 3 * 2 * 1 = 120
Final answer = 120 * 7 * 6 * 5 * 4 * 3 = 50400
Therefore, the correct answer is option D) 50400.
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In how many different ways can the letters of the word 'CORPORATION' b...
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In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?a)47200b)48000c)42000d)50400Correct answer is option 'D'. Can you explain this answer?
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