Arranging the Letters of the Word SOFTWARE

To find the number of ways the letters of the word "SOFTWARE" can be arranged such that all the vowels are together, we can treat the group of vowels (O, A, E) as a single entity. This way, we have to arrange the entity "SFTWR" and the entity "OAE" separately.

Step 1: Arrange the consonants (SFTWR)
The group of consonants in the word "SOFTWARE" is SFTWR. Since there are 5 consonants, they can be arranged among themselves in 5! = 120 ways.

Step 2: Arrange the vowels (OAE)
The group of vowels in the word "SOFTWARE" is OAE. Since there are 3 vowels, they can be arranged among themselves in 3! = 6 ways.

Step 3: Combine the arrangements
Now, we need to combine the arrangements of the consonants and vowels. Since the vowels are treated as a single entity, we can consider the consonants and the entity (OAE) as 6 distinct objects.

The consonants (SFTWR) can be arranged in 120 ways, and the vowels (OAE) can be arranged in 6 ways. Thus, the total number of arrangements is 120 * 6 = 720.

However, in each of these arrangements, the vowels (OAE) can be rearranged among themselves in 3! = 6 ways. So, we need to divide the total number of arrangements by 6 to account for this repetition.

Hence, the final number of ways the letters of the word "SOFTWARE" can be arranged such that all the vowels are together is 720 / 6 = 120.

Therefore, the correct answer is 4320.

Given