Multiple choice

Number of words using letter of $INVOLUTE$ with $3$ vowels and $2$ consonats=.............

  1. $288$
  2. $1440$
  3. $120$
  4. $2880$
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D Correct answer
Explanation

INVOLUTE has 8 letters: I, N, V, O, L, U, T, E. Vowels: I, O, U, E (4). Consonants: N, V, L, T (4). Choose 3 vowels: 4C3 = 4. Choose 2 consonants: 4C2 = 6. Total ways to choose letters = 4 * 6 = 24. Arrange 5 letters: 5! = 120. Total words = 24 * 120 = 2880.

AI explanation

The word INVOLUTE has 8 distinct letters, consisting of 4 vowels (I, O, U, E) and 4 consonants (N, V, L, T). To form a 5-letter word with 3 vowels and 2 consonants, we select 3 vowels from the 4 available and 2 consonants from the 4 available, then arrange these 5 distinct chosen letters. The required number of ways is (4 C 3) multiplied by (4 C 2) multiplied by 5 factorial, which equals 4 times 6 times 120. The result is 2880.

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