1. A quiz consists of 5 multiple-choice questions, each has three possible answers. In how many different ways can the quiz be answered if an answer is chosen for each question? I said 5 x 3 = 15 It's 3^5 = 243 possibilities. If the answers for each are A, B & C, you can have A A A A A A A A A B A A A A C A A A B A A A A B B A A A B C A A A C A A A A C B A A A C C etc. You can see there are more than 15. -------------------------------- 2. In how many ways can three different math books and four different English books be arranged in a row if the books for each subject are placed together? 3 x 4 = 12 With the math books first, the 1st book can be 1 of 3, the 2nd 1 of 2, then 1 = 3*2*1 = 6 For the English books, it's 4*3*2 *1 = 24 6*24 = 144 Then the English books can be first, --> 288 ways. ---------------------------- 3. In how many different ways can three finalists be selected from 15 job applicants for a second round interview? 15 x 3 = 45 It's 15*14*13 = 2730 ---------------------- 4. Fifteen dogs enter a Goofy Dog contest. In how many different ways can a champion, a first runner-up, and a second runner-up be selected? 15 x 3 = 45 Same as #3, 2730
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