Multiple choice

In how many different ways can the letters of the word INTEL be arranged so that the vowels always come together?

  1. 48

  2. 35

  3. 32

  4. 31

  5. 28
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A Correct answer
Explanation

INTEL has 5 letters (I, N, T, E, L). Vowels are I, E. Treat (IE) as one unit. We have 4 units: (IE), N, T, L. These can be arranged in 4! = 24 ways. The vowels (IE) can be arranged in 2! = 2 ways. Total = 24 * 2 = 48.

AI explanation

The word INTEL has 5 distinct letters, including the 2 vowels I and E. Treat the two vowels as a single connected unit, which reduces the total units to arrange to 4. These 4 units can be arranged in 4 factorial ways, which equals 24. The two vowels within the unit can be arranged in 2 factorial ways, so multiplying 24 by 2 gives 48 ways.

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