combinatorics: how many different railway tickets needed?

[tsh44]

A railway has 30 stations. On each ticket, the departure station and the destination station are printed. How many different tickets are possible?

I did 30 x 29 and got 720.

However I do not know how to get this other part.

if a ticket can be used in either direction between 2 stations, how many different tickets are needed?

The anser is supposed to 435. How do you arrive at that answer?

 

[daon]

\(\displaystyle \L \frac{n!}{r! (n-r)!}\,\, \rightarrow \,\, \frac{30!}{2! (30-2)!} \\ = \frac{30 \cdot 29}{2} = \frac{870}{2} = 435\)

 

[stapel]

Re: combinatorics: how many different railway tickets needed

I did 30 x 29 and got 720.

How?

Please clarify. Thank you.

Eliz.