4. Each of the four regions in the design below needs to be colored a different color, chosen from red, orange, yellow, green, blue, indigo, and violet. A. Let X be the set of different colorings of these regions. Compute XI. B. Suppose this design is made into a token, manufactured of colored plastic. Two such tokens are indistinguishable if one can be rotated or flipped to coincide with the other. Let Y be the set of such tokens, and let f: X→Y be the function that inputs a colored design (as in part (a)) and outputs a colored token. The function f is n-to-one and onto. What is n? What is Y), the number of distinct tokens? 4 2 3
4. Each of the four regions in the design below needs to be colored a different color, chosen from red, orange, yellow, green, blue, indigo, and violet. A. Let X be the set of different colorings of these regions. Compute XI. B. Suppose this design is made into a token, manufactured of colored plastic. Two such tokens are indistinguishable if one can be rotated or flipped to coincide with the other. Let Y be the set of such tokens, and let f: X→Y be the function that inputs a colored design (as in part (a)) and outputs a colored token. The function f is n-to-one and onto. What is n? What is Y), the number of distinct tokens? 4 2 3
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 5SE: Answer the following questions. 5. What is the term for the arrangement that selects r objects from...
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Transcribed Image Text:4. Each of the four regions in the design below needs to be colored a different color, chosen from red, orange, yellow, green, blue, indigo, and violet.
A. Let X be the set of different colorings of these regions. Compute XI.
B. Suppose this design is made into a token, manufactured of colored plastic. Two such tokens are indistinguishable if one can be rotated or flipped to coincide with the other. Let Y be the set of
such tokens, and let f: X→ Y be the function that inputs a colored design (as in part (a)) and outputs a colored token. The function f is n-to-one and onto. What is n? What is Y), the number of
distinct tokens?
3
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