Need a little bit of help with this one.
How many 10 letter 'words' can be constructed which have no repeated letters and at least 8 consonants?
where 'word' is defined as any combination of the 26 letters of the english alphabet, and by consonant, (obviously) a letter of the english alphabet that are not either a,i,u,e, or o.
This is where I am at:
We need to choose the positions for the 8 consonants which is $c(10,8)$
Then we need to choose the 8 consonants which I think is $p(21,8)$? (not sure about this one)
Choose the remaining 2 letters: We have already used 8 letters so we only have 18 letters to choose from so $p(18, 2)$
What else needs to be calculated? Do we need to choose the position of the remaining 2 letters?