A small high school holds its graduation ceremony in the gym. Because of seating constraints, students are limited to a maximum of four tickets to graduation for family and friends. Suppose 30% of students want four tickets, 25% want three, 25% want two, 15% want one, and 5% want none.

a. Write a simulation for 150 graduates requesting tickets, where students’ requests follow the distribution described above. In particular, keep track of the variable T = the total number of tickets requested by these 150 students.
b. The gym can seat a maximum of 410 guests. Based on your simulation, estimate the probability that all students’ requests can be accommodated.