Multiple choice

The number of ways that the letters of the word 'HOTEL' can be rearrange so that the vowel many come together is

  1. 24

  2. 48

  3. 20

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The word HOTEL has 5 letters: H, O, T, E, L. Vowels are O and E. Treat (OE) as one unit. We have 4 units: H, T, L, (OE). These can be arranged in 4! = 24 ways. The vowels (OE) can be arranged in 2! = 2 ways. Total = 24 * 2 = 48.

AI explanation

The word HOTEL has 5 distinct letters, including the two vowels O and E. Using the gap method, arrange the 3 consonants first, which can be done in 3 factorial, or 6, ways. This arrangement of 3 consonants creates 4 gaps (including the ends) where the vowels can be placed together as a single unit. There are 4 places to put this vowel block, and the two vowels can be arranged among themselves in 2 factorial, or 2, ways. Multiplying these together gives 6 times 4 times 2, which equals 48.

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