Multiple choice

The number of arrangements that can be formed out of GANESHPURI SO that (ii) the vowels are always together is :

  1. 6! 4!

  2. 7! 3!

  3. 7! 4!
  4. $7! 8^p4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

GANESHPURI has 10 letters: G, A, N, E, S, H, P, U, R, I. Vowels are A, E, U, I (4). Consonants are G, N, S, H, P, R (6). Treating vowels as one unit, we have 6 + 1 = 7 units. These can be arranged in 7! ways. The 4 vowels can be arranged among themselves in 4! ways. Total = 7! * 4!.

AI explanation

The word GANESHPURI contains 10 letters, of which 4 are vowels (A, E, I, U) and 6 are consonants. To keep the vowels together, treat them as one single block, which results in 7 items to arrange (6 consonants plus the vowel block). These 7 items can be arranged in 7 factorial ways, and the 4 vowels within their block can be arranged in 4 factorial ways. The total number of arrangements is therefore 7! multiplied by 4!, which is written as 7! 4!.

Keep practicing — related questions