Notation What does the symbol ! represent? The five starting players of an NBA basketball team can stand in a line 5! different ways, so what is the actual number of ways that the five players can stand in a line?

In Exercises 5 and 6, use the Fundamental Counting Principle.

6. The state of Virginia's license plates have three letters and four digits. Assuming that any letter or digit can be used, how many different license plates are possible?

How many possible outcomes are there if you roll 5 dice?

How many options are there for license plates with any three letters (A-Z) followed by any 3 numbers (0-9)?

Phone numbers are 10 digits long. How many possible phone numbers are there if the 1^st and 4^th numbers can't be 0?

Soccer Shootout In the FIFA Women’s World Cup 2019, a tie at the end of two overtime periods leads to a “shootout” with five kicks taken by each team from the penalty mark. Each kick must be taken by a different player. How many ways can 5 players be selected from the 11 eligible players? For the 5 selected players, how many ways can they be designated as first, second, third, fourth, and fifth?

Jumble Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. The letters MHRHTY were included in newspapers on the day this exercise was written. How many ways can those letters be arranged? Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.

Expected Value in North Carolina’s Pick 4 Game In North Carolina’s Pick 4 lottery game, you can pay $1 to select a four-digit number from 0000 through 9999. If you select the same sequence of four digits that are drawn, you win and collect $5000.

a. How many different selections are possible?

Using the Fundamental Counting Principle In Exercises 37-40, use the Fundamental Counting Principle.

37. Menu A restaurant offers a $15 dinner special that lets you choose from 6 appetizers, 12 entrées, and 8 desserts. How many different meals are available when you select an appetizer, an entrée, and a dessert?