The word LEADING has 7 different letters.
If the vowels E, A, I always come together, then they are considered as one letter.
Then, we have to arrange the letters of LEADING as LNDG (EAI).
Now, 5 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