combinatorics: how many different railway tickets needed?

tsh44

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Sep 4, 2005
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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?
 
\(\displaystyle \L \frac{n!}{r! (n-r)!}\,\, \rightarrow \,\, \frac{30!}{2! (30-2)!} \\ = \frac{30 \cdot 29}{2} = \frac{870}{2} = 435\)
 
Re: combinatorics: how many different railway tickets needed

tsh44 said:
I did 30 x 29 and got 720.
How?

Please clarify. Thank you.

Eliz.
 
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