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.

How many ways can a baseball coach arrange the order of 9 batters if there are 15 players on the team?

A florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums. Each small arrangement contains one rose, three daisies, and three chrysanthemums. Each medium arrangement contains two roses, four daisies, and six chrysanthemums. Each large arrangement contains four roses, eight daisies, and six chrysanthemums. One day, the florist noted that she used a total of 24 roses, 50 daisies, and 48 chrysanthemums in filling orders for these three types of arrangements. How many arrangements of each type did she make?

In how many different ways can two letters be chosen from the letters A, B, C, D, E, F, and G? (The order of the two letters is not important.)

If a man has 4 sweaters and 5 pairs of slacks, how many different outfit can he wear?

A palette of water color paints has 3 shades of green, 3 shades of blue, 2 shades of red, 2 shades of yellow, and 1 shade of black. How many ways are there to choose one shade of each color?

In a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How many musicians play either piano or trumpet?

A forester is making a gasoline-oil mixture for a chainsaw engine. The forester has 2 gallons of a mixture that is 32 parts gasoline and 1 part oil. How many gallons of gasoline should the forester add to bring the mixture to 50 parts gasoline and 1 part oil?

DISCUSS: Complementary Combinations Without performing any calculations, explain in words Why the number of ways of choosing two objects from ten objects is the same as the number of ways of choosing eight Objects from ten objects. In explain Why c(n,r)=c(n,nr)

There are 10 applicants for three sales positions at a department store. All of the applicants are qualified. In how many ways can the department store fill the three positions?