So I am having some trouble with a few parts of my homework problem. The question gives us 3 vowels (A,E,O) and 4 consonants (B,C,D,F).
a) How many ways can you make a 7 letter word if each letter can only be used once. (Word doesn't have to be real). This was easy, as the answer is just 7!
b) If the vowels have to be together and the consonants have to be together?
My approach: 3 vowels can be rearranged in 3! ways and 4 consonants in 4! ways, and the vowels can be leading or ending, so the total is 3! * 4! * 2!.
c) If the vowels have to be together?
My approach: 3 vowels in 3! ways, and can be rearranged in 5! ways.
d) If B and C have to be together, but no other vowels or consonants can be together?
My approach: I first tried making a word that starts with a consonant, and then alternating between vowel and consonant, while keeping B and C last. My other word started with a vowel then a consonant, then B and C, then vowel, consonant and the vowel. This is all I could think of, and I'm not sure how the math checks out on this.
Thanks for any help!