How many 7-letter words (with or without meaning) can be constructed using <strong>ALL</strong> the letters of the word CAPITAL so that <strong>ALL</strong> consonants come together in each word?

Explanation

Vowels: A, A, I. Consonants: C, P, T, L. Treating all 4 consonants as 1 block, we have 4 items to arrange (the block + A, A, I), which can be done in 4!/2! = 12 ways. The 4 consonants can be arranged inside their block in 4! = 24 ways. Total = 12 \times 24 = 288.

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