Multiple choice

In how many ways can the word ESPECIALLY be arranged such that all the vowels always come together?

  1. 42600

  2. 25200

  3. 10080

  4. 30240

  5. 29242
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

ESPECIALLY has 10 letters: E, S, P, E, C, I, A, L, L, Y. Vowels are E, E, I, A (4). Consonants are S, P, C, L, L, Y (6). Treat vowels as one block. Total arrangements = (7! / 2!) * (4! / 2!) = 2520 * 12 = 30240.

AI explanation

The word ESPECIALLY has 10 total letters, with 4 vowels (E, E, I, A) and 6 consonants (S, P, C, L, L, Y). We group the 4 vowels into a single block, which means we are arranging this block and the 6 consonants, making 7 objects. Because the consonant L repeats twice, these 7 objects can be arranged in 7! / 2! ways. The vowels within their block can be arranged in 4! / 2! ways because E repeats twice, so the total is (7! / 2!) multiplied by (4! / 2!), which is 2520 times 12. The result is 30240.

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