Please use combination and factorial to calculate and fully explain

(10 marks) Three soldiers (named A, B, and C) have to decide between themselves, which one goes on a dangerous mission. They decide to take turns drawing straws; there are 5 long straws and 2 short straws. Whoever picks a short straw first must go on the mission. They will take turns drawing straws in the following sequence ABCCCBA ABCCCBA etc. For each soldier (A, B, and C), what is the probability that they end up picking the first short straw? Once a short straw is drawn, they can stop picking.

a) (5 marks) Suppose they draw straws without replacement. Note: This means after a straw is drawn it is not available for the next pick. Note: In this scenario they will certainly determine who goes on the mission after the first 5 draws.

b) (5 marks) Suppose they draw straws with replacement. Note: This means after a long straw is drawn it is replaced and available for the next pick. Note: In this scenario, draws continue indefinitely according to the drawing order described above until someone eventually picks a short straw.