difficult probability questions (1 Viewer)

[mrbunton]

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.

 

[braintic]

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

 

[mrbunton]

(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

 

[braintic]

Then (a) (i) is 3^5

 

[mrbunton]

yup. b)iii) is the most difficult btw

 

[InteGrand]

yup. b)iii) is the most difficult btw

There is a way to do it without needing to do any calculations.

 

[mrbunton]

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.