12. A true-false test has eight questions. How many different permutation of answers can the teacher create if five answers are true and three answers are false? 15. a) How many ways can 9 coins (3 dimes, 4 quarters, and 2 loonies) be arranged in a line? State any assumptions you are making. 13. The Chief Wakas Totem Pole, located in Vancouver's Stanley Park, b) What if the line must begin and end with a loonie? State any represents the talking stick and characters in an Owikeno (Kwakiutl) assumptions you are making. story. In the photograph below, the Chief Wakas Totem Pole is on the 16. Sam, Nunzio, and 8 of their friends are playing outside on a hot right. The figures, from the top down, are Thunderbird, Killer Whale summer day. How many ways can 10 freezies (3 grape, 2 lime, and Wolf, Wise One, Huxwhukw (a mythical bird), Bear, and Raven. 5 orange) be distributed among the 10 children if Sam must have lime and Nunzio must have grape? 17. How many permutations are possible using all the letters of the word STATISTICS for each condition described below? You must start with A and end with C. b ) The two I's must be together. Closing 18. Consider the words BANANAS and BANDITS. Explain why there are 12 times the number of permutations possible using all the letters of BANDITS compared to the number of permutations possible using al Chief Wakes Totem all the letters of BANANAS. ica is pictured, far built as a ceremonial Chief Wakes's house Extending Vancouver Island. 19. A Rubik's cube can be thought of as a grid in three dimensions. How many routes are there from the top rear vertex of the cube to the lower front vertex of the cube, if each route must be as short as possible and follow the grid lines? 20. How many ways can 20 soccer players on a travelling team be assigned to hotel rooms for each situation? a) There are only 10 double rooms. b) There are 5 quadruple rooms. 21. A bag contains three identical red marbles and three identical white marbles. Four marbles are drawn out of the bag and arranged in a row from left to right. a) Suppose a new totem pole is created using different permutations a) How many different arrangements might be made? of all seven figures. How many different arrangements of these b) What is the likelihood that the arrangement is, from left to right, figures on the pole are possible? red, white, white, red? b) Suppose another new totem pole is to include these seven figures: two of Thunderbird and two of Wolf, as well as Killer Whale, Wise totem pole ? One, and Bear. How many ways can these figures be arranged on a 14. Explain why men = n! cannot be used to determine the number of arrangements of a group of n items when there are a identical items in the group and a