## Description

Problem 1. (25 points)

How many bitstrings of length 10 contain either five consecutive 0s or five consecutive 1s?Problem 2. (25 points)

A computer network consists of six computers. Each computer is directly connected to zero or more of the

other computers. Show that there are at least two computers in the network that are directly connected to

the same number of other computers.Problem 3. (25 points)

How many ways are there for a horse race with four horses to finish if ties are possible?

Note: any number of the four horses may tie.

Problem 4. (25 points)

1. How many different strings can be made from the word PEPPERCORN when all the letters are used?

2. How many of these strings start and end with the letter P?

3. In how many of these strings (from part 1) are the three letter Ps consecutive?