Practice:

  a) How many 6 character passwords are there that only use lowercase letters?



  b) How many 6 character passwords are there that start with 2 digits and end with 4 lowercase 			letters?



  c) How many 5 or 6 character passwords are there that use only lowercase letters?



  d) How many people do you need in a room before there are two people that were born in the same 		month?





  1: How many ways can people have 3 initials?




  2: How many bit strings are there of length six or less?  Bonus: How can you write this very 			 	simply?




  3: How many bit strings of length seven begin with two 0s AND end with three 1s?




  4: How many bit strings of length seven either begin with two 0s OR end with three 1s?




  5. How many people do you need in a room before you can guarantee that two people have names that 	start with the same letter?




  6. How many people do you need in a room before you can guarantee that two people have the same 		birthday?




  7. How many people do you need in a room before you can guarantee that there is someone that was born on New Years Day?











  8. Six cooks are preparing dishes in the kitchen in an Italian restaurant.  There are seven waiters that pick up the food and bring it to the tables in the dining area.  How many different routes are possible (by way of different people) for the food to get to the patrons?




  9.  How many 6-character passwords are there, using only lowercase letters, that begin with 'r'?




  10.  How many 6-character passwords are there, using only lowercase letters, that end with 't'?




  11.  How many 6-character passwords are there, using only lowercase letters, that begin with 'r' 		or end with 't'?




  Challenge: 
  12.  How many people do you need in a room before you can guarantee that there are four from the 		same state?




  13. Can you come up with a formula for figuring these kinds of problems out?




  14. Using that formula, can you tell how many people you need before you can guarantee that there 	are 18 from the same state?



  //The following questions are regarding playing cards, without jokers
  15.  How many cards must you draw before you are guaranteed to have two of the same suit?




  16. How many cards must you draw before you are guaranteed to have three of the same value?




  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?