Question

How many different letter arrangements can be made from the letter of the word EXTRA in such a way that the vowels are always together?

• A. 48
• B. 60
• C. 40
• D. 30

Answer 1

The Correct Option is A

To solve the problem of finding how many different arrangements can be made from the letters of the word "EXTRA" where the vowels are always together, follow these steps:

1. Identify the vowels and consonants in the word "EXTRA". The vowels are E and A, and the consonants are X, T, and R.
2. Treat the vowels E and A as a single unit. This creates a new set of elements to arrange: {EA, X, T, R}.
3. Determine the number of arrangements of these 4 elements. Since they are distinct, use the factorial of the number of elements: 4! = 24.
4. Within the "EA" unit, arrange the vowels. The number of ways to arrange E and A is 2! = 2.
5. Multiply the number of arrangements of step 3 by the number of arrangements in step 4 to get the total number of arrangements: 24 * 2 = 48.
6. Thus, the total number of different letter arrangements with vowels always together is 48.

Order	Factorial Calculation
Consonants and Vowel Group	4! = 24
Vowel Arrangement	2! = 2
Total Arrangements	4! * 2! = 48