Question

The number of words that can be formed using the letters of the word VOWEL such that vowels always remain together is:

• A. \( 60 \)
• B. \( \mathbf{48} \)
• C. \( 36 \)
• D. \( 45 \)

Hint:

When certain letters must remain together, treat them as a single unit and multiply by their internal arrangements.

Answer 1

The Correct Option is B

VOWEL has 5 letters. Vowels = O, E ⇒ keep them together as a block. Treat OE as one block → blocks = [OE, V, W, L] = 4 items ⇒ \( 4! \) ways. Within the block OE: 2! ways to arrange. \[ \text{Total} = 4! \cdot 2! = 24 . 2 = \boxed{48} \]