# The Counting Principle

Which of the following events would be considered dependent events?

It rains in Seattle and it does not rain in New York City.

Sandra rolls a die four times.

Stephanie chooses an outfit to wear out of four shirts and three pairs of pants.

After Kevin picks a popsicle flavor out of a box, Rachel picks a popsicle flavor.

Which of the following events would be considered independent events?

Two cards are randomly picked from a standard deck of cards.

Carlos has math, chemistry, and English homework. He chooses what order to do the homework in.

A student answers five multiple-choice questions with A, B, C, or D

A group of people choosing what food to eat at a buffet restaurant.

Darien is buying flowers for his mother on mothers day. He has choice between white roses, red roses, or yellow roses and a choice between white daisies,pink daisies, or yellow daisies. How many different combinations of flowers can he buy.

6

9

15

54

Cammie is choosing an outfit to wear to school. She has a choice between a blue shirt, a red shirt, or a green shirt. She can wear a pair of jeans or a skirt. Which of the following tree diagrams best represents the number of outfit choices she has.

 A. B. C. D.

In how many ways can a casting director choose a male and female lead from six female actresses and three male actors?

18

9

362880

72

A restaurant offers the following lunch menu options. Customers are allowed to pick one item from each of the four categories.

 Main Course Vegetables Beverages Desserts Ham Chicken Fish Beef Green beans Broccoli Mixed Veggies Potatoes Coffee Tea Milk Juice Cake Pie Ice Cream

How many different combinations could customers use for their meal?

15

192

4

144

Brandon gave Jennifer his phone number, but Jennifer forgot the last three digits of the number. She knows the last digit is definitely not a 7. The first seven digits are shown below.

823-555-2_ _ _

How many different telephone numbers are possible using the information she knows?

3

30

900

1000

Eight performers are participating in open mic night at a restaurant. How many different ways are there to schedule their appearances?

8

36

8,064

40,320

How many different 5-digit codes are possible using a keypad with 10 digits where no digit may be used more than once?

50

100,000

30,240

3,628,800

A camp counselor and 5 campers are sitting at a picnic table. The counselor must sit in the middle and one camper who tends to start trouble must sit to her immediate right. How many different ways are there for the rest of the campers to be seated?

5040

720

120

24

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