2. The game of Mastermind requires players to select a \"code\" consisting of a

Question

2. The game of Mastermind requires players to select a "code" consisting of a sequence of four pegs, each of which may be of any of six colors: red, green, blue, yellow, white, and black. Note, the sequence is read from left to right, so "Blue, Red, Black, Red" is considered a different code from "Red, Blue, Blue, Black". (a) [1 point How may different codes are there? Indicate your reasoning. (b) 2 points) How may different codes are there that have two or more pegs of the same color? Indicate your reasoning. (c) [2.5 points If a code is randomly selected, what is the probability that it has NO red pegs? Indicate your reasoning along with your calculations and formulas.

Explanation / Answer

4 pegs to to be chosen out of 6 colors

a)total different codes=6^4=1296

b)no. of codes of all pegs to be different =P(6,4)=360

so, no. of codes that have two or more pegs of same color=1296-360=936

c) To count the ones with no reds ,we will count the ones with four non-red pegs

There are 5^4=625 codes with no red pegs

so, probability=625/1296=0.4823

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