Question

How many words each of two vowels and three consonants can be formed from the letters of the word "UNIVERSAL" ?

• A. 7000
• B. 7200
• C. 7400
• D. 7800

Answer 1

The Correct Option is B

The word "UNIVERSAL" consists of 9 letters, including 4 vowels (U, I, E, A) and 5 consonants (N, V, R, S, L). We need to form words using 2 vowels and 3 consonants. Follow these steps to find the number of possible words:

1. Select 2 vowels from the 4 available vowels:
   Total choices for vowels = C(4, 2) = 6
2. Select 3 consonants from the 5 available consonants:
   Total choices for consonants = C(5, 3) = 10
3. Arrange the selected 5 letters (2 vowels and 3 consonants) to form a word:
   Total arrangements of the letters = 5! = 120

Therefore, the total number of words that can be formed is calculated by multiplying these values:

Number of words = 6 (vowels) × 10 (consonants) × 120 (arrangements) = 7200

Hence, the correct answer is 7200.