Couldn't you have used spaces?
"how many strings of six lowercase letters of the english alphabet contain>
a)exactly one vowel? ans:122523030>"
Okay there are 5 consonants in that string and 21 consonants. What does the "fundamental counting principle" tell you about the number of possiblities? There are
5 vowels so 5 possible values for that vowel. And, then, there are 6 places in the string that vowel could go. How many possible strings does that give?