In how many different ways can the letters of the word 'LEADING' be arranged so that the vowels always come together?

Problem restatement
Count arrangements of 'LEADING' where the vowels form one adjacent block.

Given data

• Word: L, E, A, D, I, N, G (7 distinct letters).
• Vowels: E, A, I (3 vowels).
• Consonants: L, D, N, G (4 consonants).

Concept/Approach
Block the vowels as [V]; arrange [V] with the 4 consonants (5 items), then permute vowels inside [V].

Step-by-step calculation
Arrange 5 items: 5! = 120 Permute vowels (E, A, I): 3! = 6 Total arrangements = 120 × 6 = 720

Verification/Alternative
All letters are distinct; no division by factorials for repeats is needed.

Final Answer
720