$6$ persons enter the train during the journey with $6$ different tickets of the same class. How many different sets of ticket may they have had?

Question

A train going from Cambridge to London stops at nine intermediate stations. $6$ persons enter the train during the journey with $6$ different tickets of the same class. How many different sets of ticket may they have had?

My attempt is as follows:-

Attempt $1$:

So as there are $10$ possible destinations (London + $9$ intermediate stations) , so there will be $10$ different tickets.

So as 6 people have 6 different tickets, so different sets of tickets which they can have will be $\displaystyle{10\choose 6}$. But actual answer is $\displaystyle {45\choose 6}$. So I tried some different approach.

Attempt $2$:

May be the uniqueness of the ticket is suppose to be determined by the source and destination.

There are $10$ sources and $10$ destinations, hence no of different tickets will be $\left(10+9+8\cdots\cdots+1\right)=55$.

So different sets of tickets which they can have will be $\displaystyle{55\choose 6}$, but not matching the actual answer $\displaystyle {45\choose 6}$

What am I missing here?

Answer 1

I believe that if the passengers enter the train 'during' the journey, Cambridge station is not a possible source.

Answer 2

Give $11$stops there are ${11 \choose 2}=55$ trips that one can take. Then you choose six of the possible tickets in ${55 \choose 6}$ ways. I agree with you.