The following exercise involves distinguishable permutations.

A group of thirty students is taking a field trip to a science museum. Three vans are available for transporting the students. The first van has room for eight students, and the other two vans each have room for eleven students. In how many different ways can the students be assigned to the vans?

These exercises involve counting permutations. A ship carries five signal flags of different colors. How many different signals can be sent by hoisting exactly three of the five flags on the ship's flagpole in different orders?

These exercises involve the Fundamental Counting Principle. A couple have seven children: three girls and four boys. In how many ways can the children be arranged for a holiday photo if the girls sit in a row in the front and the boys stand in a row behind the girls?

Each of the 20 shoppers in a shopping mall chooses to enter or not to enter the Dressfastic clothing store. How many different outcomes of their decisions are possible?

These exercises involve counting subsets. Each of 20 shoppers in a shopping mall chooses to enter or not to enter the Dressfastic clothing store. How many different outcomes of their decisions are possible?

Solve these exercises by using the appropriate counting principle(s). From a group of ten male and ten female tennis players, two men and two women are to face each other in a men-versus-women doubles match. In how many different ways can this match be arranged?

(a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? (b) How many of these are odd numbers? (c) How many are greater than 330?

In how many ways can five students be seated in a row of five chairs if Jack insists on sitting in the first chair?

This exercise involve counting permutations. A pianist plans to play eight pieces at a recital. In how many ways can she arrange these pieces in the program?

These exercises involve the Fundamental Counting Principle. A company's employee ID number system consists of one letter followed by three digits. How many different ID numbers are possible with this system?

How many different tables of 4 can you make from 16 potential bridge players? How many different tables if 4 of the players insist on playing together?

Solve these exercises by using the appropriate counting principle(s). A group of 22 aspiring thespians contains 10 men and 12 women. For the next play, the director wants to choose a leading man, a leading lady, a supporting male role, a supporting female role, and eight extras-three women and five men. In how many ways can the cast be chosen?

This exercise involve distinguishable permutations. In how many different ways can four pennies, three nickels, two dimes, and three quarters be arranged in a row?

A game of concentration (memory) is played with a standard $52$-card deck. How many potential two-card matches are there (e.g., one jack "matches" any other jack)?