# Thread: Probability: How many train stations if there are 552 tickets for different journeys?

1. ## Probability: How many train stations if there are 552 tickets for different journeys?

Hi, I am new at this forum and I want to get some help solving a math exam about Probability. Here's the exam:

How many train stations are in a railway line if there's 552 tickets for different journeys?

2. Originally Posted by Metskendo
Hi, I am new at this forum and I want to get some help solving a math exam about Probability. Here's the exam:

How many train stations are in a railway line if there's 552 tickets for different journeys?
There are two difficulties in answering this. The first is that I'm not sure what the question means. Was there any more information in the context?

Possibly it is assuming that any pairing of an initial station and a destination station counts as a different "journey" (but it's the same "journey" and "ticket" if taken at a different time or by a different person!), so you are being asked to count the number of different ordered pairs (x, y), where x and y are any two stations. If there are N stations, how would you calculate the number of such "journeys"? Then you could solve an equation that says this expression is equal to 552. This will give a reasonable answer, so I guess it's what the problem means.

The second difficulty is that you've said nothing about what work you have done, or what you have learned, so I can't be sure what kind of help will be appropriate. If what I've said isn't enough, please show what you have tried, and also tell us what sort of topics the test covers (say, about how to count things like this).

3. Originally Posted by Dr.Peterson
There are two difficulties in answering this. The first is that I'm not sure what the question means. Was there any more information in the context?

Possibly it is assuming that any pairing of an initial station and a destination station counts as a different "journey" (but it's the same "journey" and "ticket" if taken at a different time or by a different person!), so you are being asked to count the number of different ordered pairs (x, y), where x and y are any two stations. If there are N stations, how would you calculate the number of such "journeys"? Then you could solve an equation that says this expression is equal to 552. This will give a reasonable answer, so I guess it's what the problem means.

The second difficulty is that you've said nothing about what work you have done, or what you have learned, so I can't be sure what kind of help will be appropriate. If what I've said isn't enough, please show what you have tried, and also tell us what sort of topics the test covers (say, about how to count things like this).
Dear Dr.Peterson, firstly I want to thank you for your reply. Actually there are no more information in the context (or maybe I made a mistake at translating), but I can interpret it more clear:

How many train stations are in a railway line, if for different journeys there's 552 different tickets !

The point is that even I can't understand the context, so I've been thinking for a while if there's any mysterious info that we can understand from the context, because it seems that all we know is that there are 552 different tickets for different journeys.

Thanks!

4. Is your daughter able to communicate with us directly? I would like to ask her whether she's been studying number sequences and formulas for adding numbers in a set. For example, to add counting numbers (up to some value n), the formula is:

1 + 2 + 3 + … + n = n(n+1)/2

I would ask her to draw two dots on paper. It ought to be clear that there are two different trips, for a rail line with two stations (one trip in each direction).

On a rail line with three stations, there are six different trips (three in each direction). Four stations yields twelve different trips. Continue increasing the number of stations (up to about seven) -- drawing and counting the different trips for each. Then, try to find a formula that generates the trip counts, given some number of stations.

Such a formula can be used to find how many stations are needed for 552 different trips.