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Question: question 1 module outcome 1 a company wishes to offer...

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Question 1 (Module Outcome #1): A company wishes to offer employees a choice for their personal identification numbers (PIN). Each pin must be 4 characters in length and cannot contain repeated characters. The first and second characters can be any digit 0, …, 9; the third and fourth character can be any of the 5 symbols chosen from {@,#,!,%,&}. How many PINs are possible?
Question 2 (Module Outcome #2): Numeric passwords of length r consist of n digits from {0,1,2,…,9}. Digits may be not repeated (e.g., 1178 is a not a permissible password of length 4). Find the smallest value of r such that the number of possible passwords is greater than 2,000,000.
Question 3 (Module Outcome #3): A game of mistle consists of 5 teams; 4 teams lose and 1 team wins. Twenty-nine teams enter a mistle tournament. For each round of competition, games are played with 5 teams and any team who cannot be assigned to a game gets a “bye” to the next round. How many games must be played to determine the tournament champion?
Question 4 (Module Outcome #4): Six digits are chosen randomly.
a.) What is the probability that all six digits are the same?
b.) What is the probability that five or more of the digits of the same?
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