1. ## difficult probability questions

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.

2. ## Re: difficult probability questions

(a) Can't be answered unless we know whether the boxes are distinguishable, and whether the items are distinguishable.

3. ## Re: difficult probability questions

Originally Posted by braintic
(a) Can't be answered unless we know whether the boxes are distinguishable, and whether the items are distinguishable.
both items and boxes are distinguishable

4. ## Re: difficult probability questions

Then (a) (i) is 3^5

5. ## Re: difficult probability questions

yup. b)iii) is the most difficult btw

6. ## Re: difficult probability questions

Originally Posted by mrbunton
yup. b)iii) is the most difficult btw
There is a way to do it without needing to do any calculations.

7. ## Re: difficult probability questions

Originally Posted by InteGrand
There is a way to do it without needing to do any calculations.
ya;if u do solve it using calculations it will be nearly impossible; unless it is through induction. I still believe its a step up from the probability usually done in highschool.

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