Okay, the letters A E I O U can be place in these three places: _ _ _.
There are 5 possibilities for the first blank: - _ _.
Once that one is filled, there are four letters left to fill the second blank: - - _.
Once both of the first two spots are full, then there are 3 letter choices for the last blank: - - -.
To find out the number of possibilities, multiply the first possible number of choices times the second times the third, so: 5 * 4 * 3 = 60 possibilities.
There are four cities to choose from and three reports to do. So, it's the same as above.
There are three places: _ _ _.
When the first is full, there are 3 cities left: - _ _.
Then the first and second are full, there are 2 cities left: - - _.
Then there are only two options to fill that third space.
So 4 * 3 * 2 = 24 possibilities.
