f3 1. The following data was collected from the records of 150 park-goers at Canada's Wonderland: 2-"? people liked the Leviathan it} people liked the Behemoth 59 people liked the Top Gun 45 people liked the Leviathan and the Behemoth 31 people liked the Behemoth and the Top Gun 35 people liked the Leviathan and the Top Gun 15 people liked all three a. Draw a 'v'enn diagram to illustrate the data Is. How manv park-goers didn't like anv of the three rides? a. How manv park-goers liked exactlv one ride? 2. Consider the following sets, and then answer: 5 = {all letters of the alphabet} A = {letters in the word PABALLELDGRAM} B = {vowels in the word SQUARE} a. List the elements in set A A = { b. List the elements in set B a = { o. Draw a 1v'enn diagram showing all the elements of sets A and B d. Shade in A u B on vour diagram e. nlA u as = 3. This question refers to the universal set S from question #2. 5 = {letters in the alphabet}. a. How mam; subsets are there of set S? b. How many subsets are there with 4 elements? o. How many subsets contain the letter A? 4. What is the value of term E- in row 31 of Pascal's Triangle? 5. Rewrite the expression (15?) in an equivalent "choosy\" of the form (1:) E. Rewrite the expression (15?) using Pascal's Formula 1 What row of Pascal's Triangle has the following sum? (3) + (711) + G) + ........ +(11 E 1) + (2) = 32353 8. TRUE or FALSE? Provide an example to demonstrate the property if the statement is true OR clearly justify your thinking if the statement is false. (Hint: Draw a diagram if that helps). If A C B', and B' C S , then A C S 2In this section, there are three parts in question. Some parts must be done by all students, and some parts haye a choice: General question (- all students should answer thls [it Further calculations *6 you have a choloe to {iil Comprehension 8! analysis (- ...or this either answer this... m Note #1: if you unswer both options. l will only morlr your response to port {I} on the left. Note #2: tn all questions, you do not need to euuluote unol onsI-Her, just set them up 9. The student council at Happy Valley High School consists of E- boys, ti girls, and 3 nonbinary students. In how many ways can they form a liye-person social committee if: a. There are no restrictions? {1 b. The committee must haye 2 boys. 2 girls. and 1 nonhinary student? {2 c. The committee must be all boys or all girls? {2 {3 d. [it The committee must haye at least one . {ii} 0f the non-binary students. one boy, at least one girl. and at least one identities as neither male nor female, nonhinary student? and two identify as both male and female. Create a two-set yenn diagram that illustrates this scenario. KQ1 1098765432A 10. Given a standard deck of 52 cards (see image), a poker hand is dealt containing 5 cards. KQ 1 1098765 4 3 2 A a. In how many ways could your hand have exactly three face cards? /2 KQ1 10987 6 5 43 2 A b. In how many ways could you get two pairs? (the fifth card is different from the others) /3 c. (i) A "straight flush" is when all five c. (ii) The value of cards in Poker are such cards are in order and of the same suit. that A is worth more than K, and AA is In how many ways could you get a worth more than KK. So why is AK not straight flush? Assume an Ace is equal worth more than KK? Justify /2 to 1. mathematically. A OR11. Gill orders a hot dog from a fancy new sandwich shop, and he has the following options for toppings: Condiments: ketchup, mustard, relish, hot sauce Veggies 31 Things: onions, hot peppers, sauerkraut, oliyes, bacon bits Cheese: grated cheese, nacho cheese a. In how many ways could Gill dress his dog if he's open to anything, he just doesn't want a bare hotdog? {2 b. The shop is testing out some new snacks and drinks, which they're selling at a discount. They're almost sold out, but the following is left: - 3 bags of kettle chips I: 2 bags of artisanal popcorn - 5 cookies {2 In how many ways could Gill choose some snacks? c. {i} Gill has some strong opinions about c. {iii If T = {toppings}, which of the above hot dog sandwiches: he feels that a scenarios {part a. or part b.) inyolyes hotdog should never have more than considering all possible subsets of T? fiye items or it gets messy. How many which subset is not included in your {2 combinations are possible? answer? Explain. 12. The students in our class decide that they would like to form study groups that will meet up on Teams on weekends. In order make sure eyeryone's included, Ms. Wills sets up the groups. Since there are 21 students in the class, Ms. Wills makes one group of E- and three groups of 5. All groups will meet on Saturdays at 1pm. a. In how many ways can the students split up into the four groups if she forms the group of 5 first? .32 b. {i} If Gavin and Dylan want to be h. {ii} Would your answer to part a. change together [in any group]. how many if Ms. 1Iiiirills formed a group of 5 first? groups are possible? m Why or why not? f4 c. {iii Would your answer to part a. change if one person in each group is named the leader? Why or why not