Four people are to be arranged in a row to have their picture taken. In how many ways can this be done?

An automobile manufacturer has four colors available for automobile exteriors and three for interiors. How many different color combinations can he produce?

In a digital computer, a bit is one of the integers [math]\{0,1\}[/math], and a word is any string of 32 bits. How many different words are possible?

What is the probability that at least 2 of the presidents of the United States have died on the same day of the year? If you bet this has happened, would you win your bet?

There are three different routes connecting city A to city B.

How many ways can a round trip be made from A to B and back? How many ways if it is desired to take a different route on the way back?

In arranging people around a circular table, we take into account their seats relative to each other, not the actual position of any one person. Show that [math]n[/math] people can be arranged around a circular table in [math](n - 1)![/math] ways.

Five people get on an elevator that stops at five floors.

Assuming that each has an equal probability of going to any one floor, find the probability that they all get off at different floors.

A finite set [math]\Omega[/math] has [math]n[/math] elements. Show that if we count the empty set and [math]\Omega[/math] as subsets, there are [math]2^n[/math] subsets of [math]\Omega[/math].

A more refined inequality for approximating [math]n![/math] is given by

Write a computer program to illustrate this inequality for [math]n = 1[/math] to 9.

A deck of ordinary cards is shuffled and 13 cards are dealt.

What is the probability that the last card dealt is an ace?