9 (C) (a) You give your students the following problem: "You just bought 30 beads of which 18 are gold and identical and 12 are silver and identical. You want to line them up in a row. How many different arrangements of the beads can you make?" Elizabeth solves the problem by finding the number of distinguishable permutations of 30 objects, 18 alike of one kind and 12 alike of another kind. That is, she uses the result of the previous problem. Natalie solves the problem by finding the number of combinations of 30 different objects taken 18 at a time. Who is correct? (b) Does the number of permutations of n objects, r alike of one kind and n - r alike of another kind, always equal the combinations of n different objects taken r at a time? Explain.
9 (C) (a) You give your students the following problem: "You just bought 30 beads of which 18 are gold and identical and 12 are silver and identical. You want to line them up in a row. How many different arrangements of the beads can you make?" Elizabeth solves the problem by finding the number of distinguishable permutations of 30 objects, 18 alike of one kind and 12 alike of another kind. That is, she uses the result of the previous problem. Natalie solves the problem by finding the number of combinations of 30 different objects taken 18 at a time. Who is correct? (b) Does the number of permutations of n objects, r alike of one kind and n - r alike of another kind, always equal the combinations of n different objects taken r at a time? Explain.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CT: Chapter Test
Problem 4CT: Over the past year, John has purchased 30 books. a In how many ways can he pick four of these books...
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