Consider a backgammon match with 25 games, each of which can have one of two outcomes: win (1 point), or loss (0 points). Find the number of all possible distinct score sequences under the following alternative assumptions. (a) All 25 games are played. (b) The match is stopped when one player reaches 13 points.

Louis wants to carpet the rectangular floor of his basement the basement has an area of 864 square feet the width of the basement is 2/3 its length what is the length of lewis's basement

Atravel agent is booking a trip to england, scotland, ireland, and france for a group of senior citizens. the agent sent surveys to the group, asking which countries they would like to visit, in order, and created the shown preference schedule (e = england, i = ireland, s = scotland, f = france). which country is the condorcet winner? number of votes 15 12 16 19 1st f e e i 2nd e s i s 3rd s i s e 4th i f f f 1. scotland 2. england 3. france 4.ireland

Jack is considering a list of features and fees for current bank: jack plans on using network atms about 4 times per month. what would be jack’s total estimated annual fees for a checking account with direct paycheck deposit, one overdraft per year, and no 2nd copies of statements? a. $44 b. $104 c. $144 d. $176