In how many different ways can the letters of the word LEADING be arranged in such a way that the vowels always come together?
360
480
720
5040
Explanation:
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 = 5] letters can be arranged in 5! = 120 ways.
The vowels [EAI] can be arranged among themselves in 3! = 6 ways.
$\therefore$ Required number of ways = $\left(120 \times 6\right)$ = 720.