The question gives us 3 vowels (A,E,O) and 4 consonants (B,C,D,F). a) How many ways can you make a

Ryker Stein

Ryker Stein

Answered question

2022-05-29

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?
c) If the vowels have to be together?
d) If B and C have to be together, but no other vowels or consonants can be together?

Answer & Explanation

szilincsifs

szilincsifs

Beginner2022-05-30Added 15 answers

Let's start by simplifying the problem a little bit. Let A, E, and O be represented by "V" and let (BC), D, and F be represented by "C". Then we see that we can arrange these letters as "VCVCVC" or "CVCVCV". This tells us that, assuming all vowels and all the consonants are the same (and here we are treating (BC) as one consonant), there are 2 ways to arrange the letters.
But, the vowels and consonants are not all the same. There are 3! to arrange the distinct vowels and there are 3! ways to arrange the consonants (again treating (BC) as one consonant).
This gives 2*6*6=72 ways to arrange the letters. Remember that we treated (BC) as a single letter. We can flip (BC) and write it as (CB) and that gives us twice as many combinations. Therefore, we have 72*2=144 ways to arrange the letters so that BC are together and no other consonant pair or vowel pair are adjacent.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?