Please do this by matlab

6. (Birthday Problem, Lecture 7) In a group of n randomly chosen people, what is the prob- ability that everyone has a different birthday? (a) Find this probability by hand. (b) Let n = 30. Write a script that generates a group of n people randomly and determines if there are any matches. (c) Modify the script above to run a number of simulations and numerically calculate the sought-after probability. Try 1000, 10000, and 100000 simulations. Compare the result with the analytical calculation done in the previous part