Exercise 10 (p. 177) in Harris

4. Exercise 10 (p. 177) in Harris, Hirst & Mossinghoff. [20p+20p] A hungry math major visits the school's cafeteria and wants to know the num- ber of ways sk to take k servings of food, including at least one main course, an even number (possibly zero) of side vegetables, an odd number of rolls, and at least two desserts. The cafeteria's food can be distinguished only in the coarsest way: Every dish is either a main course, a side vegetable, a roll, or a dessert. There is an unlimited supply of each kind of dish available. (a) Express Skxk as a rational function. (b) Prove that ] Tkal SK 3 =(1+1)+(*') (. Note. Recall that [x] means x rounded down to the next integer, while [x] means x rounded up to the next integer. 4. Exercise 10 (p. 177) in Harris, Hirst & Mossinghoff. [20p+20p] A hungry math major visits the school's cafeteria and wants to know the num- ber of ways sk to take k servings of food, including at least one main course, an even number (possibly zero) of side vegetables, an odd number of rolls, and at least two desserts. The cafeteria's food can be distinguished only in the coarsest way: Every dish is either a main course, a side vegetable, a roll, or a dessert. There is an unlimited supply of each kind of dish available. (a) Express Skxk as a rational function. (b) Prove that ] Tkal SK 3 =(1+1)+(*') (. Note. Recall that [x] means x rounded down to the next integer, while [x] means x rounded up to the next integer