PART A: Short Answer: For each question, write your final answer on the solution page provided. No marks will be given for any work. (2 marks each) 1. James is looking for something to wear to impress his friends. His outfit will consist of a shirt, tie, pants, and shoes. His shirts are yellow, red and white. His ties are red and green. His pants are red, tan, black, and green. His shoes are black, blue, white and brown. How many different outfits does he possibly have? 2. Twelve students are running for president, vice-president, treasurer and secretary at a high- school. They can only be named to one of the positions. In how many different ways can the student be elected? For the next two questions: How many committees of 5 teachers can be selected from 7 male teachers and 5 female teachers if: 3. The committee must contain at least 2 female teachers? 4. Mrs. Besse and Mr. Quast must not be included? 5. Moving only right and down, how many pathways are there from A to B? B 6. Assume a car license plate consists of 7 characters. The first 3 characters can be any of the letters from A to M, but no letter can be repeated. The next 3 characters can be any of the digits from 1 to 6, but can be repeated. The last character can be any of the letters X, or Z. How many license plates are possible? 10. 11. 12. In how many different ways can the letters of the word INTENTIONAL be arranged if the first letter must be an I7? Determine the number of different five-letter arrangements that can be formed with the letters GUIDEPOST if the last two letters must not be vowels. From a standard deck of cards a 5-card hand is dealt. Calculate the number of hands that contain 4 diamonds and 1 black King. Using a standard deck of cards, determine the number of 5-card hands which contain at most one King. A hockey team of 18 players is chosen from 24 available players. How many ways can this occur if Jeff and Brent cannot both be chosen? At the most recent Grad Committee meeting everyone shook hands with everyone else in the room. If there was a total of 136 handshakes, how many people were in the room? \fPART B: WRITTEN RESPONSE: (4 marks each) Show all your work. Marks will not be given for the solution only. 3(n-1)! 13. Solve algebraically for n: (n3)! W 7 14. Consider a standard deck of 52 cards. How many five card hands can occur that contain at least two diamonds