Multiple choice

How many words can be formed using all the let ters of the word SPECTRA so that all the vowels are always together?

  1. 720

  2. 360

  3. 1440

  4. 180
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Word SPECTRA has 7 letters: S, P, E, C, T, R, A. Vowels are E, A. Treat (EA) as one unit. Now we have 6 units: S, P, C, T, R, (EA). These can be arranged in 6! ways. The vowels (EA) can be arranged in 2! ways. Total = 720 * 2 = 1440.

AI explanation

The word SPECTRA has 7 letters with 2 vowels (E and A) and 5 consonants. Using the grouping method, we bundle the 2 vowels together as one single unit. This gives us 6 total units to arrange, which can be done in 6 factorial ways. The 2 vowels can be arranged within the bundle in 2 factorial ways, making the total arrangements 720 multiplied by 2, which equals 1440.

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