a) [5×1 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 (15novels, 10 history books, and 5 math books). In how many ways canyou:
i. Get a bunch of four books to give to a friend?
ii. Get a bunch of three history books and seven novels to giveto a
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