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In the game of Mastermind, one player selects a code by inserting any combination of four pegs in a row of four hidden holes. There are six colors of pegs to choose from. The second player tries to guess the code by repeatedly inserting four pegs in a row and receiving feedback from the codemaker on the number of pegs of the correct color and the number of pegs in the correct position. Suppose the codemaker first selects four pegs for the code from a large supply of six colors, then determines the order the pegs will be placed in the four holes. 1) How many ways may the codemaker select the four pegs for the Mastermind code? 2) How many different Mastermind codes are possible

In the game of Mastermind, one player selects a code by inserting any combination of four pegs in a row of four hidden holes. There are six colors of pegs to choose from. The second player tries to guess the code by repeatedly inserting four pegs in a row and receiving feedback from the codemaker on the number of pegs of the correct color and the number of pegs in the correct position. Suppose the codemaker first selects four pegs for the code from a large supply of six colors, then determines the order the pegs will be placed in the four holes. 1) How many ways may the codemaker select the four pegs for the Mastermind code? 2) How many different Mastermind codes are possible

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In the game of Mastermind, one player selects a code by inserting any combination of four pegs in a row of four hidden holes. There are six colors of pegs to choose from. The second player tries to guess the code by repeatedly inserting four pegs in a row and receiving feedback from the codemaker on the number of pegs of the correct color and the number of pegs in the correct position. Suppose the codemaker first selects four pegs for the code from a large supply of six colors, then determines the order the pegs will be placed in the four holes.

1) How many ways may the codemaker select the four pegs for the Mastermind code?

2) How many different Mastermind codes are possible?

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