Please need done asap

1. A student residence meal plan offers the following meal choices for Friday night: Appetizer Main Course Dessert Beverage Soup Veggie Burger Fruit Bowl Milk Salad Lasagna Ice Cream Apple Juice Hamburger Chocolate Cake Coffee Chicken Fingers Tea a. [1 mark] |n how many ways could a student order a meal consisting of one choice from each column? b.[2 marks] How would the solution change if one of the item from any one column of the menu is no longer available? What is the resulting total number of ways of ordering a meal? 2. A handmade necklace has 12 different beads with visible clasp a. [1 mark] How many distinct necklaces can be made? b. [2 marks] How many distinct necklaces can be made if there is no visible clasp? Would it even change? 3. [2 marks] A baseball team has 13 potential batters. How many batting orders of nine players can be made, such that batter A and batter B must bat and be together and in the first four positions? 4. Eight runners are entered in a track meet, and have equal ability. What is the probability that a. [1 mark] they will finish in alphabetical order? b. [2 marks] Eva will finish first or Emma will finish second? c. [1 mark] Eva and Emma will not finish back-to-back? 5. [3 marks] A lottery ticket contains six different numbers, chosen from 1 to 39. The winning ticket will match all six numbers in the correct order, plus a bonus number, which may match the other six numbers. The second prize matches the six winning numbers in the correct order, but not the bonus number. What is the probability of not winning first or second prize? u. I, nun-1:, nu unv-vuu 1. [2 marks] There are four boys and five girls in a club. Describe two situations, one where the fundamental counting principle would be used and one where the rule of sum would be used. . [2 marks] The 13 players on a volleyball team are to line up for a team photograph. The seven shortest players will be in the front row. The remaining players will be in the back row. The coach will be in the back row on either the left or right end or in the middle. How many different arrangements are there for the team photo? . [4 marks] A serial number uses the following pattern 000nnooooo where represents a digit from 1 to 9, . represents a consonant and represents a vowel. How many different serial numbers can be generated if repetition is not permitted? Justify your answer. . [2 marks] In how many ways could 10 people be seated at a circular table if the two hosts should not sit together? . [1 mark] What is the probability that at least two people in a group of 30 people will have the same birthday? . [2 marks] In a card game Concentration, the cards of a standard deck are laid out in four rows of 13 cards. A player turns over two cards hoping they match. What is the probability that the four aces will be in the four corners