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The number of arrangements of the letters in the word ‘FAILURE’ so that vowels are coming together is?
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Number of Arrangements of the Letters in the Word 'FAILURE' with Vowels Together
First, let's analyze the word 'FAILURE' and identify the vowels and consonants present in it. The word 'FAILURE' has three vowels (A, I, E) and four consonants (F, L, R, U).
Arranging Vowels Together
To arrange the vowels together, we can consider the three vowels (A, I, E) as a single entity. Therefore, we have 4 entities to arrange - (Vowels)AE, F, L, R, U.
Number of Ways to Arrange Entities
Now, the number of ways to arrange these 4 entities is 4!, as there are 4 entities to arrange. However, within the vowels entity, there are 3! ways to arrange the vowels (A, I, E) among themselves.
Number of Ways to Arrange the Entire Word
Therefore, the total number of ways to arrange the word 'FAILURE' with vowels together is 4! * 3!.
Calculating the Number of Arrangements
4! = 4 x 3 x 2 x 1 = 24
3! = 3 x 2 x 1 = 6
So, the total number of arrangements of the letters in the word 'FAILURE' with vowels coming together is:
24 x 6 = 144
Therefore, there are 144 different arrangements of the letters in the word 'FAILURE' where the vowels (A, I, E) come together.
First, let's analyze the word 'FAILURE' and identify the vowels and consonants present in it. The word 'FAILURE' has three vowels (A, I, E) and four consonants (F, L, R, U).
Arranging Vowels Together
To arrange the vowels together, we can consider the three vowels (A, I, E) as a single entity. Therefore, we have 4 entities to arrange - (Vowels)AE, F, L, R, U.
Number of Ways to Arrange Entities
Now, the number of ways to arrange these 4 entities is 4!, as there are 4 entities to arrange. However, within the vowels entity, there are 3! ways to arrange the vowels (A, I, E) among themselves.
Number of Ways to Arrange the Entire Word
Therefore, the total number of ways to arrange the word 'FAILURE' with vowels together is 4! * 3!.
Calculating the Number of Arrangements
4! = 4 x 3 x 2 x 1 = 24
3! = 3 x 2 x 1 = 6
So, the total number of arrangements of the letters in the word 'FAILURE' with vowels coming together is:
24 x 6 = 144
Therefore, there are 144 different arrangements of the letters in the word 'FAILURE' where the vowels (A, I, E) come together.
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The number of arrangements of the letters in the word ‘FAILURE’ so that vowels are coming together is?
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The number of arrangements of the letters in the word ‘FAILURE’ so that vowels are coming together is? 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 The number of arrangements of the letters in the word ‘FAILURE’ so that vowels are coming together is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of arrangements of the letters in the word ‘FAILURE’ so that vowels are coming together is?.
The number of arrangements of the letters in the word ‘FAILURE’ so that vowels are coming together is? 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 The number of arrangements of the letters in the word ‘FAILURE’ so that vowels are coming together is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of arrangements of the letters in the word ‘FAILURE’ so that vowels are coming together is?.
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