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

Step-by-step solution

The word DELHI consists of 5 letters: 3 consonants (D, L, H) and 2 vowels (E, I). The arrangement of letters in the word is Consonant-Vowel-Consonant-Consonant-Vowel. Since the positions of vowels and consonants must remain unchanged, the consonants can only be placed in the 1 st, 3 rd, and 4 th positions, and the vowels can only be placed in the 2 nd and 5 th positions. The 3 consonants can be arranged in their 3 positions in 3! ways. The 2 vowels can be arranged in their 2 positions in 2! ways. Total number of ar