Question

1. How many arrangements can be created by lining up 9 flags in a vertical column if

a. each flag has a different color?

b. 3 flags are white, 2 are red, and 4 are blue?

c. 3 flags are white, 2 are red, 4 are blue, and 2 red flags cannot be next to each other.

2. You have a set of 20 blank cards. On each card you print either a circle, a square, a triangle, or a diamond. How many different sets of 20 cards are possible if order of the printed cards is not important and

a. all blank cards are white and identical?

b. each blank card had a different color?

c. each blank card has a different color, and exactly 10 cards got a square printed on them?

3. An ice cream store has 21 different flavors, 6 different kinds of sauce, and 10 different toppings. How many different kinds of large sundae 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 one, two or three toppings, where each topping can be used only once and the order of the toppings does not matter?

Answer 1