Give reasons

1. (48 points) True/False Questions To get credit, you must give brief reasons for each answer! 1446 Let a be the last digit of your student ID, and assume there are 365 days in one year. Then, in any group of (360 + a) students, there must be at least two that have the same birthday (same month and same day) T F in term ?? T F Let a be the last digit of your student ID. Suppose your friend is willing to try every item listed in the menu, which includes steak, fish, pasta, burgers, and specialty pizza. If he/she will only have one item for each meal, without repeating any item for ((a mod 3) +3) meals. The number of ways to have ((a mod 3) +3) consecutive meals is 60. AuB is bo Leta be the last digit of your student ID, and suppose there are (a +5) cafeterias at NYIT, the number of ways of having breakfast, lunch and dinner is 125 T F is Leta be the last digit of your student ID, and suppose you just got a free ticket for a boat ride, and you can bring along 2 friends. Unfortunately, you have (a + 5) friends who want to come along. The number of different groups of friends you can take with you is 10. T F T F Let a be the last digit of your student ID, and suppose there are (a + 15) students in the class, who will vote for Salten Hall and Vending Machine Each student will and can only vote once. The total number of possible voting results (in terms of Salten Hall vs. Vending Machine) is 465