Counting Rules: a. In how many ways can first, second, and third prizes be awarded in a contest with 34 contestants? b. How many ways can a committee of 3 people be selected from a club that has 19 members? c. How many ways can you make a 5 digit password that can be any number (including zero) or letter (not case sensitive)? d. How many ways can you order 6 people standing in line?
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Question a asks for the number of ways to award first, second, and third prizes to 34 contestants. This is a permutation problem because the order of selection matters (first prize is different from second prize, etc.). Show more…
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Madhur L.
Answer each of the following problems. SHOW ALL NECESSARY WORK to fully justify each of your answers. a) There are 35 students on a football team. They must elect 3 students to serve as captains. How many different ways could the election turn out? b) You go to the video store to rent some movies for the weekend. There are 1000 movies available, and you want to select 3 of them. How many ways can you make your choices? c) A club has 20 members. i. In how many different ways could the club choose a president and a vice-president? ii. In how many different ways could the club choose two co-presidents? d) Four different novels and five different biographies are placed on a shelf. In how many ways can they be arranged if all the biographies must be kept together? e) Suppose three people are in a room. What is the probability that there is at least one shared birthday among these three people?
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