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Andrea has just purchased a five-digit combination lock that allows her to set up her own combination. She can use the numbers through for her combination, and she must use five digits.

  1. How many five-digit combinations can she make so that no digit is repeated?

    Although the problem says 'combination' this is actually a permutation
    because the order you enter the numbers in the combination lock matters.

  2. How many five-digit combinations are possible if she can repeat the digits, but cannot use the same digit twice in a row?

    Since this is a special case you can use a decision chart.
    How many choices does she have for each position?