Question 3 (a) An ice cream parlor has 28 different flavors, 8 different kinds of sauce, and 12 toppings. (i) Compute the number of kinds of small sundaes are there if a small sundae contains one scoop of ice cream, a sauce, and a topping. (b) (c) (ii) Compute the number of kinds of large sundaes are there if a large sundae contains three scoops of ice cream, where each flavor can be used more than once and the order of the scoops does not matter; two kinds of sauce, where each sauce can be used only once and the order of the sauces does not matter; and three toppings, where each topping can be used only once and the order of the toppings does not matter. A company needs to assign unique project codes to a set of five new projects. Each project code is created using the first letter of the project's name. The names of the five projects are: Alpha (A), Beta (B), Gamma (G), Delta (D), and Epsilon (E). (i) (ii) (iii) Compute the number of ways can the company assign a unique 5-letter project code using all five letters (A, B, G, D, E). If the company wants to assign only a 3-letter project code (using any combination of A, B, G, D, and E) for each project, compute the number of different 3-letter project codes can be created without repeating any letter. Compute the number of ways the 3-letter project codes can be created that start with B and do not repeat any letters. - Solve the following recurrence relation, an = 5an-1 6an-2, with initial conditions of a 2, and a₁ = 7.