Problem $1$: Change Simulation A charity event is organized in Dubai, and a ten dirham "donation" is required per attendee. Suppose that every person who comes to the event pays with either a $10$ Dhs note or a $20$ Dhs note. The team that collects payment at the door has a limited number of $10$ Dhs notes to give as change. Suppose $10$ people come to the event, and everyone pays for their "ticket." Half of the attendees pay with a $10$ Dhs note, and the other half pay with a $20$ Dhs note. Answer the following questions. $1$a$.$ How many $10$ Dhs notes must the team start with to ensure that they can give a change to everyone who pays with a $20$ Dhs note, regardless of the order in which people arrive? $1$b$.$ What could be the total number sequence of possible arrivals of $5$ people with $10$ Dhs note and $5$ people with $20$ Dhs note? $1$c$.$ Perform a data generation through simulations to calculate the probability that the team will run out of $10$ Dhs notes if they start with only $1$ note and attendees arrive randomly. Explain each step of your code.