(Birthday problem reloaded!) Consider a group of 10 individuals, each of whom has their birthday on a randomly chosen day of the year, out of 365 days (i.e. without leap years). Answer the following questions: (You do not have to calculate the actual values; simplified expressions in terms of facto- rials/permutations/combinations suffice.) (a) (3 points) Find the probability that all 10 individuals have their birthday on De- cember 25. (b) (3 points) Find the probability that exactly 5 individuals (i.e., any 5 out of 10) have their birthdays on December 25. (c) (2 points) Find the probability that all 10 individuals have their birthdays on the same day (any day of the year). (d) (4 points) Find the probability that all these individuals have birthdays in a se- quence; e.g. (Dec 30, Dec 31, Jan 1, Jan 2, ... , Jan 8). Note that sequences can "wrap around" the year, i.e. Jan 1 is considered as coming after Dec 31, in a loop. Also note than any individual can have any of the birthdays in the sequence, i.e. the individuals do not follow a specific order in the sequence. (e) (4 points) Find the probability that all these individuals have their birthdays in September (September has 30 days). (f) (4 points) Find the probability that exactly 5 individuals (i.e., any 5 out of 10) have their birthdays in September