Counting
The singer Bruno Mars has a song that goes, "You can count on me like one, two, blah." What number replaces the "blah" in the actual song?
What is "three"?
This is the number you would get if you take the number of students in our class, add 2023, multiply by 0, and subtract 5.
What is -5?
This is the result of subtracting C(100,30) from C(100,70). Hint: It's the most laidback integer there is, neither positive nor negative.
What is 0?
This is how many subsets there are of the set {a, b}. Hint: There were four main members of the Beatles, and they sang the song, "We all live in a yellow submarine." In fact, the title of this category "We all live in a yellow subset" was loosely based on this song by the Beatles. If your group can all sing a portion of the chorus together, score 100 points extra.
What is 4? (And, nice singing.)
It's famous STEM women time! Score 100 points for each female you can name who was a recipient of (a) a Nobel Prize or (b) the Fields Medal.
For example, who are/were Marie Curie, Jane Addams, Morther Teresa, Aung San Suu Kyi, Maryam Mirzakhani, Maryna Viazovska, Malala, Leymah Gbowee?
If you roll a single 6-sided die, this is the number of ways to get a number that is even or more than 4 (or both).
What is 4?
This is the number of ways you can hand out 20 identical cheesy gifts to your five friends at EMU. It's possible some friend(s) get none and a pigeon told me that at least one friend must get at least four.
What is C(24,4)?
From a school class of 70 boys and 45 girls, this is how many ways you could form a council of 2 boys and 2 girls (no distinct positions).
What is C(70, 2)*C(45,2)?
That singing we all just witnessed was okay, but I think that your group can make the Beatles even more proud. Sing, as a group, portions of up to 3 Beatles' songs for 100 pts each. The next group can have up to 1 more for 100 pts (if they can think of one) just so everyone has a chance to sing some Beatles.
What is "I wanna hold your hand"?
The EMU Math Club of 5 first-years, 3 sophomores, 2 juniors, and 4 seniors must create a Owenation subcommittee with 2 first-years and 1 from each of the other classes. This is the number of ways to do that.
What is 240 ways?
When rolling a green die and a red die (both 6-sided), this is the number of ways that the number showing on the green die is higher than the one on the red die.
What is 15?
Score 100 pts (up to 500) for every song that you can sing a portion of in 20 seconds (for this question, it can be any member of the group). Caveat: Each song must contain the word "love" (or a derivative) in it AND you must sing a portion of the song that has that word. Rebound teams can get up to 200 each but only have 10 seconds each.
What is "I can feel the Love."?
There are 18 students in a class, with 11 of those students being seniors. This is how many councils of 4 with exactly 2 seniors could be formed from among the class if Caleb (senior) insists he cannot be on the council with Noah (not senior).
What is C(11,2)C(7,2) - 60 councils?
Name a country that has yellow in its flag. (Score a bonus of 100 for up to 2 other such countries, but as soon as you guess an incorrect one, it's over!)
What is Germany, Belgium, Vietnam, China, etc.?
These are the trinity of Hindu gods.
Who are Brahma, Vishnu, and Shiva?
This is the chance that a 13-card hand from a deck of 52 cards contains exactly one of each of the 13 values.
What is (4^13)/C(52,13)?
Without using a calculator or looking at notes, places these in order from lowest to highest: p(10,3), C(10,3), S(10,3), and P(10,3).
p(10,3), C(10,3), P(10,3), and S(10,3).
This is the greatest value of C(100, 20), C(90, 30), C(60,40), and C(50,50) without using a calculator.
What is C(90,30)?
Given a set A with n elements, this is the subset of all relations on A that are both one-to-one and onto functions.
What is n! functions?
In polka dot poker, each player is dressed in polka dot clothing and gets 5 cards from a 52-card deck. This is the number of polka dot poker hands that have just a pair (not two pair, not three-of-a-kind, not full house).
What is C(13,1)*C(4,2)*C(12,3)*(4^3) = 1,098,240 hands?
This is the number of positive integers less than or equal to 100 that are divisible by 2, 3, or 5.
What is 74?
This is the number of ways that you can split a class of 10 students into an even number of groups. (Who's in what group matters, but the groups themselves are identical.)
What is S(10,2) + S(10,4) + S(10,6) + S(10,8) + S(10,10)?
This is the number of ways in which the questions of this Jeopardy game could be chosen (keeping the rule that you must move downward within any particular column).
What is C(25,5)*C(20,5)*C(15,5)*C(10,5)?
This is how many subsets of [90] contain only multiples of 3.
What is 2^30?
Rather than following the traditional way to open your Advent calendar, you decide to open it out of order. This is how many ways there are to open the correct door every Wednesday (and Christmas itself of course!) and an incorrect door on all other days. Note: Assume there are four Wednesdays before Christmas on that December.
What is !20 ways?