\documentclass[11pt, letter]{article}
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\usepackage{enumitem}
\usepackage[most]{tcolorbox}
\usepackage{amsmath}
\usepackage{hyperref}
\setcounter{section}{-1} 

\begin{document}
    \textbf{Submission instructions are in the homework handout. The handout is the final source of truth for instructions and question statements over this template file, which exists only for your convenience.}

    \section{Collaborators}
    \begin{tcolorbox}
        TODO: Add collaborators here.
    \end{tcolorbox}

    \newpage
    \section{CSE Plays Soccer [15 points]}
    Twelve people ($4$ students and $8$ faculty) on CSE's soccer team show up for a game.
    \begin{enumerate}[label=\alph*.]
        \item How many ways are there to choose which $4$ players will play midfield positions (for this part, you should just account for who is a midfielder and who is not)? (5 points)
        
        \item How many ways are there to assign the $4$ midfield positions by selecting players from the $12$ people who show up (for this part, account for both who plays and which of the $4$ different positions they are playing)? (5 points)
        
        \item  How many ways are there to choose which $4$ players will be midfielders if at least one of these players must be a student? (Go back to not deciding who plays which position for this part.) (5 points)
    \end{enumerate}

    \begin{tcolorbox}
        \begin{enumerate}[label=\alph*.]
            \item TODO: Your solution here
            \item TODO: Your solution here
            \item TODO: Your solution here
        \end{enumerate}
    \end{tcolorbox}

    \newpage
    \section{String cheese [24 points]}
    We want to count the number of strings of length $7$ from
    the English alphabet $\{A, B, \cdots, Z\}$ subject to a number of
    different constraints. Note that we consider the English alphabet here
    to consist of 6 {\em vowels} ($\{A,E,I,O,U,Y\}$) and 20 {\em consonants}.
    \noindent How many strings are there which...
    \begin{enumerate}[label=\alph*.]
    \item (4 points) ...are only made of vowels?
    \item (4 points) ...are only made of consonants?
    \item (4 points) ...have {\em exactly} one vowel?
    \item  (4 points) ...have {\em exactly} two vowels?
    \item (4 points) ...have at most two consonants, which may only appear in the sixth and seventh positions?
    \item (4 points) ... have at least one consonant?
    \end{enumerate}

    \begin{tcolorbox}
        \begin{enumerate}[label=\alph*.]
            \item TODO: Your solution here
            \item TODO: Your solution here
            \item TODO: Your solution here
            \item TODO: Your solution here
            \item TODO: Your solution here
            \item TODO: Your solution here
        \end{enumerate}
    \end{tcolorbox}

    \newpage
    \section{Red Riding Hood Visits Grandma [20 points]}
    \begin{enumerate}[label=\alph*.]
    \item  How many paths are there from point (0,0) to (70,140) if every step increments one coordinate and leaves the other unchanged? (4 points)
    \item   How many paths are there from point (0,0) to (70,140) if every step increments one coordinate and leaves the other unchanged and you want the path to go through (20,50)? (4 points)
    \item   How many such paths are there from (0,0) to (70, 140) that
go through (30,125), but do \textbf{not} go through (20,50)? (4 points)
    \item   How many paths are there from point (0,0) to (70,140) if every step increments one coordinate and leaves the other unchanged and the path \textbf{cannot} go through (20, 50) or (30,125)? (4 points)
    \item  How many paths are there from point (0,0,0) to (200,50,45) if every step increments one coordinate and leaves the other two unchanged? (4 points)
    \end{enumerate}

    \begin{tcolorbox}
        \begin{enumerate}[label=\alph*.]
            \item TODO: Your solution here
            \item TODO: Your solution here
            \item TODO: Your solution here
            \item TODO: Your solution here
            \item TODO: Your solution here
        \end{enumerate}
    \end{tcolorbox}

    \newpage
    \section{Three Peas Suit [10 points]}
    A new card game, Trio, is trending. Trio features a non-standard card deck of $42$ cards. The deck has $3$ suits, each of which has $14$ ranks. How many 4-card hands are there, with at least one card from each suit?

    \begin{tcolorbox}
        TODO: Your solution here
    \end{tcolorbox}

    \newpage
    \section{A very useful engineering question [6 points]}
    How many different ways are there to arrange the letters in the word \textbf{engineering}?

    \begin{tcolorbox}
        TODO: Your solution here
    \end{tcolorbox}

    \newpage
    \section{Coding [15 points]}
    \begin{enumerate}[label=\alph*.]
    \item Read the \href{https://edstem.org/us/courses/40645/lessons/66271/slides/362909}{HW1 Python Tutorial and Coding Exercises} lesson on Edstem and follow the directions to complete 5 coding exercises. Then submit all required files to HW1 [Coding] on Gradescope. You may resubmit to gradescope as many times as you like. We do not have any hidden tests for this assignment; whatever score you see on gradescope on your last submission will be your final score. (10 points)
    
    \item Read the \href{https://edstem.org/us/courses/40645/lessons/66277/slides/362939}{Edstem lesson} on Python's numpy library and write the reflection described below (be sure to finish part (a) before moving to this part). You do \textbf{not} need to complete the \emph{coding} exercises for this part. The coding exercise that is there is optional, and intended only for practice if you want it. 
    The goal of this part is to see some more advanced python features that will definitely be useful in the future, but you won't need to use frequently for this course.\\    
    After reading the lesson, write a reflection on what you felt was the most confusing numpy function and/or class to you and why. If nothing is confusing, explain which function and/or class is the most interesting to you. We will grade based on completion and effort (since this response can't be ``correct'' or ``incorrect''). We expect most responses will be 2-4 sentences. (5 points)
    \end{enumerate} 

    \begin{tcolorbox}
        \begin{enumerate}[label=\alph*.]
            \item Submit code to Gradescope.
            \item TODO: Your solution here
        \end{enumerate}
    \end{tcolorbox}
\end{document}