i) there are 5 items to be placed inside 3 boxes. how many ways can this happen. each box can contain any amount of items.

ii) if each box must contain at least one item; how many different ways are possible.

b)

i) There's 100 passengers and 100 seats in the airplane. The first passenger forgot their seat ticket, so they take a random seat, the next 98 also takes a random seat. What's the probability that the 100th person's assigned seat will be available for him?

ii)The first passenger takes a random seat. The 2nd passenger sits in his favourite seat if it is available, and if it is not available he sits in a random position. What is the probability that the last person to sit down sits in his correct seat?

iii) if all passengers attempt to take their favourite (distinct) seat; except for the first person; what is the probability of the last person getting their intended seat.