Multiple choice

In how many ways can the letters of the word DELHI be arranged while keeping the positions of vowels and consonants fixed?

  1. 6

  2. 9

  3. 12

  4. 24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

DELHI has 2 vowels (E, I) and 3 consonants (D, L, H). Vowels can be arranged in 2! = 2 ways. Consonants can be arranged in 3! = 6 ways. Total ways = 2 * 6 = 12.

AI explanation

The word DELHI has 2 vowels and 3 consonants. Since the positions are fixed, the 2 vowels can only swap places among themselves in 2 factorial ways. The 3 consonants can be rearranged among their fixed positions in 3 factorial ways. Multiplying these gives 2 factorial times 3 factorial, which is 2 times 6, resulting in 12 ways.

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