Find the number of ways of arranging the letters of the words DANGER, so that no vowel occupies odd place.

Sure, here is the step by step solution:

1. The word DANGER has 6 letters, 3 of which are vowels (A, E, and I) and 3 are consonants (D, N, G, R).

2. We want to arrange the letters so that no vowel occupies an odd place. This means that the vowels must be in the 2nd, 4th, and 6th positions, which are the even positions in the word.

3. There are 3! (3 factorial) ways to arrange the 3 vowels in the 3 even positions. 3 factorial is 321 = 6.

4. There are also 3! ways to arrange the 3 consonants in the 3 odd positions.

5. Therefore, the total number of ways to arrange the letters of the word DANGER so that no vowel occupies an odd place is 3!3! = 66 = 36.