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

Step-by-step solution

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 4! 2! because the letter A appears twice. 4! 2! = 12 The 4 consonants can be arranged among themselves in 4! ways. 4! = 24 Total number of words = 12 24 = 288 Answer: 28