The word "equation" has 8 letters, 5 of which are vowels.

There are 5 ways to choose a vowel for the 1st letter.
That leaves 7 letters to choose for the 2nd letter.
That leaves 6 letters to choose for the 3rd letter.
That leaves 5 letters to choose for the 4th letter.
That leaves 4 letters to choose for the 5th letter.
That leaves 3 letters to choose for the 6th letter.
That leaves 2 letters to choose for the 7th letter.
That leaves 1 letter to choose for the 8th letter.

Answer 5*7*6*5*4*3*2*1 = 25200

Edwin