How many 7-letter words (with or without meaning) can be...

The word CAPITAL has 7 letters.

Vowels: A, I, A (3 letters, where A is repeated twice)

Consonants: C, P, T, L (4 distinct letters)

Since all consonants must come together, they are treated as a single unit: (C, P, T, L).

Now, there are 4 units to arrange: the consonant group and the 3 vowels (A, I, A).

The number of ways to arrange these 4 units is $\dfrac{4!}{2!}$ because the letter A appears twice.

$\dfrac{4!}{2!} = 12$

The 4 consonants can be arranged among themselves in $4!$ ways.

$4! = 24$

Total number of words = $12 \times 24 = 288$

Answer: $288$