11. 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