a) [51 marks] How many permutations of the letters A, B, C, D, E, F, G that:

i. Have E in one of the first two positions?

ii. Do not have vowels on the ends?

iii. Have the two vowels before the five consonants?

iv. Have A immediately to the left of E?

v. Neither begin nor end with A?

b) [1+2+2 marks] Suppose that you have 30 different books (15 novels, 10 history books, and 5 math books). In how many ways can you:

i. Get a bunch of four books to give to a friend?

ii. Get a bunch of three history books and seven novels to give to a friend?

iii. Put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?