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fixed organization errors
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moved previous problems C1 and C2 to Problem 4 and Problem 9, respectively
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TSRichard95 authored Nov 30, 2021
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Expand Up @@ -36,18 +36,28 @@ Charlie and her girlfriend, Amber, go to lunch at a restaurant with 7 sandwiches
* if they order different sandwiches and drinks from each other?
* if they each order without concern for what the other ordered?

#### Problem 4
#### Problem 3
A small civil rights non-profit is selecting 3 of its 15 employees to form a task force focused on voting rights.
* How many such task forces could they possibly select?
* How many possibilities are there if they assign each member of the task force a unique role?

#### !! Problem 4
!! *This problem labels people (as the only way of describing them). A better description would focus on their actions or interests.*
</br>A student club focused on diversity is forming a recruitment committee consisting of 7 of its 30 members. 10 of the club’s members identify as gay and 5 identify as asexual. How many ways are there to form a recruitment committee which includes at least three members from each of these groups?

#### !! Problem 8
!! *This problem refers to 'biological sex', which at least one student found problematic.*
</br>You conduct an experiment in which you interview a large number of families, each of which has 5 children. For each family, you write down the biological sex (M for male, F for female, I for intersex) of the children, in order from oldest to youngest.
* How many possible results are there?
* Out of all the possible results, how many have exactly two I’s?
* Out of all the possible results, how many have at least one I, one F, and two M’s?

#### Problem 9
A group of students is surveyed about race and gender identity for research purposes. The survey lists 6 categories for race and 4 categories for gender. Determine how many different survey results are possible, given each of the following constraints:
* Students are allowed to check exactly 1 box under race and 1 box under gender.
* Students are allowed to check 1 or 2 boxes under race and 1 or 2 under gender.
* Students are allowed to check as many boxes as they wish (including 0).

#### !! Problem 12
!! *This problem setup lacks substance and would likely be perceived as on-the-nose by students.*
</br>Consider the set of letters, *{L, G, B, T, Q, I, A}*:
Expand All @@ -60,27 +70,17 @@ A small civil rights non-profit is selecting 3 of its 15 employees to form a tas

### Combinatorics Problems

#### Problem C1
A group of students is surveyed about race and gender identity for research purposes. The survey lists 6 categories for race and 4 categories for gender. Determine how many different survey results are possible, given each of the following constraints:
* Students are allowed to check exactly 1 box under race and 1 box under gender.
* Students are allowed to check 1 or 2 boxes under race and 1 or 2 under gender.
* Students are allowed to check as many boxes as they wish (including 0).

#### !! Problem C2
!! *This problem labels people (as the only way of describing them). A better description would focus on their actions or interests.*
</br>A student club focused on diversity is forming a recruitment committee consisting of 7 of its 30 members. 10 of the club’s members identify as gay and 5 identify as asexual. How many ways are there to form a recruitment committee which includes at least three members from each of these groups?

#### !! Problem C3
#### !! Problem C1
!! *This problem labels people (as the only way of describing them). A better description would focus on their actions or interests.*
</br>In how many ways can three men, three women, and three non-binary students stand in a circle if no two people of the same gender identity are allowed to stand next to each other?

#### Problem C4
#### Problem C2
Jon wants to choose a different three-letter name for herself to better match her pronouns. How many consonant-vowel-consonant options does she have to choose from?

#### Problem C5
#### Problem C3
A group of 12 high school students is attending queer prom together. If they want to arrange themselves into 6 couples, how many possible couple arrangements can they choose from?

#### Problem C6
#### Problem C4
The organizers of a LGBTQ rally are making pride flags. Five people all choose different flag designs from among ten; how many possible combinations of flags might they end up with?

### Formal Proof Problems
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