3. If 10 runners compete in a race, how many different ways can prizes be awarded for 1st, 2nd, and 3rd places? 4. A high school coach must decide on the lineup for the hockey team. If the roster consists of 5 wings, 4 defensemen, and 3 centers, in how many ways can a team of 1 left wing, 1 right wing, 1 center, 1 left defenseman and 1 right defenseman be formed? 5. Suppose the letters of TRAPEZOID are used to form "words". a. How many 9-letter "words" can be formed? b. How many 5-letter "words" begin with a vowel and end with a consonant? How many 3-digit numbers contain no 4's or 5's? 6. 7. How many 4-digit numbers contain at least one 6 or 77 8. How man numbers consisting of 1, 2, or 3 digits (without repetition) can be formed using the digits 1, 2, 3, 4, 5, 6 and 7? 9. In how many ways can 5 different prizes be given to any 5 of 10 people if no person receives more than 1 prize? 10. In how many different ways can you answer 8 multiple-choice questions if each answer has 4 choices? 11. How many numbers between 2000 to 7999 contain at least one 5? 12. The "home row" of a standard typewriter gives one arrangement of the letters A, S, D, F, G, H, J, K, L. If any 9 letters of the alphabet could be placed on the "home row" of a typewriter, how many arrangements of the letters would be possible? 3. A boy has 2 sports coats and 4 sweaters. Suppose he decides to wear either a sports coat, or a sweater, but not both. How many hoices does he have?