1. You will need to type in all your answers directly into Gradescope. Make sure you simplify all your

answers to integers. To simplify answers with factorials, you may find online tools such as https:

//www.wolframalpha.com/ to be helpful.

2. Double-check that you are using the correct symbols. If you choose to write your solutions digitally, the use of a

typesetting system (e.g. LATEX) is recommended. LATEX files can be created on www.overleaf.com and documentation

on how to use LATEX can be found at https://www.overleaf.com/learn/latex/Free_online_introduction_to_

LaTeX_(part_1)

3. When submitting your assignment on Gradescope make sure that pages are correctly assigned to each question in the

correct orientation. Point deductions may be applied for pages incorrectly assigned to questions.

Collaboration Policy

Collaboration is allowed. You must write your own solutions though. On every homework, you should list the names of those

students you collaborated with. Remember that copying a solution from your peer or from the internet is plagiarism and is

penalized by the GT Code of Conduct. If cheating is detected, you will receive a zero on the assignment and a report will be

filed with the Office of Student Integrity.

1. 5 points

How many numbers must be selected from the set {1, 4, 6, 8, 9, 13, 14, 16, 18, 21} to guarantee that at least one

pair of these numbers adds up to exactly 22? Simplify your answer to an integer.

2. 5 points

How many different combinations of pennies, nickels, dimes, and quarters can a piggy bank contain if it has

29 coins in it? Simplify your answer to an integer.

3. 5 points

How many different ways are there to choose 13 donuts if the shop offers 19 different varieties to choose

from? Simplify your answer to an integer.

4. 5 points each

Imagine you are drawing cards from a standard deck of 52 cards. For each of the following, determine the

minimum number of cards you must draw from the deck to guarantee that those cards have been drawn.

Simplify all your answers to integers.

a) A Straight (5 cards of sequential rank). Hint: when considering the Ace, a straight could be A, 2, 3, 4, 5 or 10, J, Q,

K, A but no other wrap-around is allowed (e.g. Q, K, A, 2, 3 is not allowed)

b) A Flush (5 cards of the same suit)

c) A Full House (3 cards of 1 rank and 2 from a different rank)

d) A Straight Flush (5 cards of sequential rank from the same suit)

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