In how many different orders can the sixteen (or twenty one) students in the class stand?

Including Mr. Gouline, there are twelve people in his advisory. He has the brilliant plan that each assembly, they will sit in a different order. How long will it take to sit in each of the arrangements? There are approximately 120 assemblies each year.

Twelve people compete in a math- off. If the teacher awards gold, silver, and bronze medals, how many ways can the prizes be distributed?

Coach Sheets needs to create a batting order from his roster of 23 players. How many choices does he have?

Nine people compete in an election where the winner is club president and the runner-up is the vice president. In how many different ways can the positions be filled?

Robby flips a coin six times. How many different outcomes are possible?

There are seven multiple-guess questions on the test at the end of this chapter (not true). Each question has five choices. How many different ways could you answer those problems?

Until recently, Maryland license plates were three letters followed by three numbers. How many different plates were possible?

In middle school, a grade consisted of a number between 70 and 100 followed by a letter (A, B, C, or D). How many different grades were possible?

How many three digit numbers contain only 1’s? How many contain no 1’s. How many contain at least one 1?

How many three digit numbers contain only 2’s and 3’s? How many contain no 2’s or 3’s? How many contain at least one 2 or one 3?

A boat used a red, blue, and green light to send signals to shore. How many different signals are possible?

Working with computers, pieces of information are transmitted in “packets” of 8 binary digits. How many different “packets” are possible?

How many different four-letter “words” could one create using the letters in GOULINE? How many of those “words” have only vowels? How many have at least one consonant?

How many different three-letter “words” can be formed using the letters in STRAW? How many of those words have no vowels? How many have at least one vowel?

A coach plans to select three captains from a group of 14 seniors. How many different ways can he choose?

Baskin Robbins has 31 flavors of ice cream. If Johnny wants a 3-scoop sundae where order does not matter and flavors cannot be repeated, how many sundaes can he order?

Baskin Robbins still has 31 flavors. Suppose they offer one, two, or three scoop sundaes where flavors can be repeated but order does not matter. How many different sundaes are possible?

Three families go to the movies together. The Smiths have four members, the Jones’s have five members, and the Johnsons have three members. How many different ways can the people sit if the families must sit together, but can sit in any order?

The math department has two single offices and two triple offices. How many ways can Mr. Gouline assign offices if each office is different but the order someone is assigned to an office does not matter?

Six couples go to a post-post-post prom breakfast (where they sit in a line at a counter). How many different ways can they sit if each couple insists on sitting together?

Mr. Heubeck will choose a group of ten juniors (from your class of 115) to represent you at a faculty meeting. How many groups are possible?

One hundred boys enter a poetry contest. There will be one winner, four runners-up, and eight “commended poets”. How many different ways can these groups be filled?

There are twelve souls on the freshman basketball team—seven forwards and five guards. How many starting lineups can Mr. Dawson create if he needs two guards and three forwards?

There are 52 cards in a standard deck. How many five-card poker hands are possible?

How many five-card poker hands are flushes (all five cards from the same suit)?

How many five card poker hands are a full house (three of one card and two of another)?

How many five card poker hands are three of a kind?