1. OBX Cart Rentals has created a website for customer access. They are trying to determine a reasonably secure number of available passwords. They have decided to allow upper case letters, lower case letters, digits (0 – 9), and the three pecial characters: $, ! ?. Find the number of possible 6 character passwords given each of the conditions (Note: you MUST simplify completely.)

1. The password must begin with a letter (either upper or lower case)

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i. repetitions permitted

ii. repetitions not permitted

2. The password must begin with a letter and end with a special character ($, !, ?):

i. repetitions permitted

ii. repetitions not permitted

2. 104 people were asked to name the online site they have purchased from this month. 40 answered they shopped at Amazon, 28 at Kohls and 59 at Costco. 12 people shopped at all three sites, 20 at Kohls and Costco and 17 at Amazon and Kohls. 20 shoppers indicated that they did not shop at any of these sites. Note: you will need to determine the number of shoppers that used Costco and Amazon.

1. Create a Venn Diagram. Note there are 8 disjoint regions. Put the count of the number of shoppers in each region.

2. How many shoppers shop at either Amazon or Kohls, but not both?

3. How many shoppers shop at exactly one store?

3. (For this problem, leave your answers in Combinatorics format – do NOT simplify). Josie

has 20 college friends that she would like to invite to join her at a concert; however, she only has 8 tickets. Since she will use one of the tickets, she needs to select seven of her friends to join her.

a. If there are no restrictions
b. Of her 20 friends, three are triplets. They will either all attend, or none.
c. Two of the friends are former roommates that no longer get along, they will not

attend together.
d. Of her 20 friends, 12 are women and 8 are men. She wants to invite more

women than men.

4. (For this problem, leave your answers in Combinatorics format – do NOT simplify). The

graduation committee has 45 men and 40 women. 3 are selected to sit on the platform with the university president.

1. How many ways can NO women be selected?

2. How many ways can at least one man be selected?

3. How many ways can 2 women and 1 man be selected?

4. How many ways can the selection be made, given the selectees a designation:

first chair, second chair and third chair

5. (For this problem, leave your answers in Combinatorics format – do NOT simplify).

Curious George is holding a bunch of balloons: 8 blue, 6 red, 5 purple and 4 yellow. He decides to let 4 of them go.

1. How many ways can he let at least 2 red balloons go?

2. How many ways can he let at most 1 yellow go?

3. How many ways can he let the balloons go so that none are yellow?

4. How many ways can he let the balloons go so that they are all the same color?

5. How many ways can he let the balloons go so that they are all different colors?

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