# determine the value in question. Note that this course emphasises going back and forth between… 1 answer below »

Question 9

Counting (38 Points)

• For each question, determine the value in question. Note that this course emphasises going back and forth between a real world problem, and a mathematical

formulation. In every case, express what you are counting as rigorously as possible.

Are you counting functions? subsets? …etc

• How many 8 character passwords can be made from the alphabet set

A = {0, 2, 4, 6, 8, a, b, c, d, e, f, g, !}

Be sure to rigorously define the set in question you are counting and how it is

generated. (2 points)

8

• In a class of 12 students, how many ways can you pair up partners? I.e., how

many groups of two can be made. Be sure to rigorously define a set that you are

counting. (2 points)

• How many possible ways can you give \$100 in increments of \$ 1 to 10 people?

(2 points)

• Consider an alphabet of 10 digits

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

. How many 8 character passwords can be made if each digit can be used at most

one time? (2 points)

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