Lets construct a diagram

_ _ _ are the spaces we need to fill to make a "word".

For the first blank we can choose any of the seven letters. The second blank, any of the six remaining letters. The last one, any of the five remaining letters. Therefore, the total number of possibilities is 7 * 6 * 5.

Now let us see how many combinations there are when the first letter must be a vowel. Out of the seven letters in METHODS, only 2 are vowels, so the first blank, choose any of the two vowels. For the second blank, choose any of the six remaining letters. For the third blank, any of your five remaining letters. Total number of combinations then is 2 * 6 * 5

(2*6*5)/(7*6*5) = 2/7

working on the next problem.