(a) Can't be answered unless we know whether the boxes are distinguishable, and whether the items are distinguishable.
a)
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.
(a) Can't be answered unless we know whether the boxes are distinguishable, and whether the items are distinguishable.
Then (a) (i) is 3^5
yup. b)iii) is the most difficult btw
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