math permutations pls help

Question

1. How many different permutations can be made from the letters "REPEATED" if the three E's are consecutive?
2. Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that a) all vowels occur together b) all the vowels do not occur together

Answer 1

1. There are 5 different positions the 3 Es can be in. Then, there are 4! possible orders for the four other letters. Thus, the number of possible orders is 5 *4! = 5! = 120
2. There are 5 consonants and 3 vowels, all different. If the three vowels are all together, there are 6 different positions for the vowels. Then, the vowels can have 3! orders and the consonants can have 5! different orders, so 6*5!*3! = 6!*3!=720*6 = 4320

all the vowels do not come together statement is ambiguous. I am interpreting this to mean that none of the vowels is adjacent to the other. Then, as there are 8 positions, you remove 2, and there are C(6,3) possible orders of the vowels. Then, once again, the lertters can be ordered in 5!*3!, so the number of possible orders is

C(6,3)*5!*3! = 20 * 120 * 6 = 14400