Hattie Plumber has 100 Goldoons to spend at Marmaduke's Sweet Shop.

Bile Balls cost 1 Goldoon. Salted Slugs cost 3 Goldoons. Toothcrackers cost 7 Goldoons.

(a) In how many ways can Hattie spend all 100 Goldoons?

(b) In how many ways can Hattie spend all 100 Goldoons, if she wants to buy exactly 40 sweets? (For the avoidance of doubt, all the items mentioned above are sweets.)