So the example I'm trying to complete is the following:
The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain:
a) exactly one vowel?
My first thought was that we pick a vowel: C(5,1) Then we pick 5 out of the 21 consonants: C(21,5) or is it 21^5 (the question doesn't state that we can't re-use consonants)
Afterwards we have to sort them into a string which I think would be P(6,6)
The result I get is way too high, the answer is supposed to be (according to the answers to odd numbers) 122,523,030.