CS161 Lab Week 9: Counting

In this lab you will practice solving counting problems. Write your answers to the following problems on paper and show the instructor your answers before leaving. The instructor will lead initial discussion of each question.

1. How many 6 character passwords are there that only use lowercase letters?
2. How many 6 character passwords are there that start with 2 digits and end with 4 lowercase letters?
3. How many 5 or 6 character passwords are there that use only lowercase letters?
4. How many people do you need in a room before there are two people that were born in the same month?
5. How many ways are there for a person to have 3 initials?
6. How many bit strings are there of length six or less?
7. How many bit strings of length seven begin with two 0s AND end with three 1s?
8. How many bit strings of length seven either begin with two 0s OR end with three 1s?
9. How many people do you need in a room before you can guarantee that two people have names that start with the same letter?
10. How many people do you need in a room before you can guarantee that two people have the same birthday?
11. How many different words of length 8 can you form in the English language such that the first letter is the same as the last letter?
12. How many different words of length 8 can you form in the English language that contain exactly one vowel?
13. How many different words of length 8 can you form in the English language that contain at least one vowel?
14. How many 6-character lowercase passwords are there, that begin with 'r' or end with 't'?
15. How many cards must you draw before you are guaranteed to have two of the same suit?
16. How many people do you need in a room before you can guarantee that there are four from the same state?
17. How many cards must you draw before you are guaranteed to have a spade?
18. How many cards must you draw before you are guaranteed to have two kings?