vowels come together

Taking the whole string of vowels of the word as a letter, there are 6 letters.So possible arrangements are 6!. But the vowel string has 3! permutations. So possible number of permutations are $\boxed{3!6!}$

"Software" has 3 vowels and 5 consonants.

The number of ways that the vowels can be arranged is 3! = 6

The number of positions that the the vowels can occur while grouped together is 6 because the group of vowels can occur like so: AAA----- , -AAA----, --AAA--- etc...

Note: We also have to take into account the number of ways that the 5 consonants can be arranged in which is 5! = 120

Times all the variables we get: 6 * 120 * 6= 4320 number of permutations.