Fundamental Counting Principle

The tree diagram shows the outcomes of rolling a die and flipping a coin.  
How many total outcomes are there?  

• 6
• 12
• 24
• 36

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.9

Which of the following situations is represented by this tree diagram?

• 3 shirt options, 6 pants options, and 12 shoe options
• 3 shirt options, 2 pants options, and 2 shoe options
• 2 shirt options, 3 pants options, and 1 shoe option

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.9

Tree Diagram

• A written list of all possible outcomes
• A description of all possible outcomes
• A drawing with branches of all possible outcomes

Tags

CCSS.7.SP.C.8

The cafeteria is serving three kinds of sandwiches:  tuna (T), chicken, (C), and peanut butter (P).  They are also serving a choice of two drinks:  milk (M) or water (W).  Which shows the complete set of possible combinations?

• TW, CW, PW
• TW, TM, TC, CW, PW
• TW, TM, CW, CM, PW, PM
• TCP, MW

Tags

CCSS.3.OA.A.1

CCSS.3.OA.A.3

If you draw a random card from a standard deck of cards, how many possible outcomes?

• 13
• 26
• 52
• 54

Tags

CCSS.HSS.CP.A.1

An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream.  A customer gets to choose a cone and a type of ice cream.   How many events are described here?

• 1
• 2
• 3
• 93

Tags

CCSS.3.OA.A.1

CCSS.3.OA.A.3

CCSS.3.OA.C.7

The cafeteria has 2 choices of salads, 3 choices of entrees, and 2 choices of beverages. How many meal combinations are available and why?

• 7 because 2 + 3 + 2
• 12 because 2 x 3 x 2

Tags

CCSS.7.EE.B.3

Three students are scheduled to give oral reports on Monday. In how many ways can their presentations be ordered?

• 3 x 2 x 1 = 6

• 3 x 3 x 3 = 27

• 3 + 3 + 3 = 9

• 3 + 2 + 1 = 6

Tags

CCSS.HSS.CP.B.9

In how many ways can the first five letters of the alphabet be arranged if each letter is used only once?

• 5 x 4 x 3 x 2 x 1 = 120

• 5 x 5 x 5 x 5 x 5 = 3125

• 26 x 26 x 26 x 26 x 26 = 11881376

• 5 + 5 + 5 + 5 + 5 = 25

Tags

CCSS.HSS.CP.B.9

The letters A, B, C, and D are used to form four-letter passwords for entering a computer file. How many passwords are possible if letters can be repeated?

• 4 x 4 x 4 x 4 = 256

• 4 x 3 x 2 x 1 = 24

• 4 + 4 + 4 + 4 = 16

• 4 + 3 + 2 + 1 = 10

Tags

CCSS.HSS.CP.B.9