How many binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string?  Briefly explain your answer.

Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number.  Show all your work.

A 100-page document is being printed by four printers. Each page will be printed exactly once. Suppose that the first and the last page of the document must be printed in color, and only two printers are able to print in color. The two color printers can also print black-and-white. How many ways are there for the 100 pages to be assigned to the four printers. Hint: Use the product rule.