In how many way different ways can be letters of the word ‘SOFTWARE’ be arranged in such a way that the vowels come together

To solve this problem, we need to consider the word 'SOFTWARE' as a combination of consonants and vowels.

Step 1: Identify the vowels and consonants in the word 'SOFTWARE'. The vowels are 'O', 'A', 'E' and the consonants are 'S', 'F', 'T', 'W', 'R'.

Step 2: Consider all the vowels as a single letter. So, the word 'SOFTWARE' becomes 'SFTWR(OAE)'. Now, we have 6 letters (5 consonants + 1 vowel group).

Step 3: These 6 letters can be arranged in 6! (6 factorial) ways.

Step 4: However, the vowels (OAE) can be arranged among themselves in 3! (3 factorial) ways.

Step 5: Therefore, the total number of ways the letters of the word 'SOFTWARE' can be arranged such that all vowels are together is 6! * 3! = 720 * 6 = 4320 ways.