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.

MATLAB: An Introduction with Applications
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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, ralike of one kind and n r alike of another
kind, always equal the combinations of n different objects taken r at a time? Explain.
Transcribed Image Text: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, ralike of one kind and n r alike of another kind, always equal the combinations of n different objects taken r at a time? Explain.
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