Multiple choice

Directions: Study the following set of questions carefully and answer the questions given below. Using all the letters of the word LINEAR.How many different words can be formed that start and end with vowel?

  1. 126

  2. 108

  3. 144

  4. 216

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word LINEAR has 6 letters: 3 vowels (I, E, A) and 3 consonants (L, N, R). To start and end with a vowel, choose 2 vowels for the ends (3 * 2 = 6 ways) and arrange the remaining 4 letters in the middle (4! = 24 ways). Total = 6 * 24 = 144.

AI explanation

The word LINEAR has 6 letters with 3 vowels (I, E, A) and 3 consonants, and since all letters are distinct, there are no repetitions to divide out. To form a word that starts and ends with a vowel, we arrange the 2 vowels at the ends in 3P2 ways, which is 6 ways. The remaining 4 letters can be arranged in the middle in 4! ways, which is 24 ways. Multiplying these gives 6 times 24, which equals 144. The result is 144.

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