How many different ways can six letters of the word TRIANGLE be arranged if the vowels must alternate with consonants? Show full work explaining how you got the answer. code example

Example: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

The word 'LEADING' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.