The question:

Alfonso and Colin each bought one raffle ticket at the state fair. If $50$ tickets were randomly sold, what is the probability that Alfonso got ticket $14$ and Colin got ticket $23$?

According to [this](https://instructure-uploads.s3.amazonaws.com/account_21740000000000001/attachments/1246022/HW%2013.2%20KEY.pdf?response-content-disposition=attachment%3B%20filename%3D%22HW%2013.2%20KEY.pdf%22%3B%20filename%2A%3DUTF-8%27%27HW%252013.2%2520KEY.pdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJDW777BLV26JM2MQ%2F20180521%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20180521T234515Z&X-Amz-Expires=86400&X-Amz-SignedHeaders=host&X-Amz-Signature=50b4ccaaf1c64ea2b83c2363c2d34b279b26b32fcd3a45b3d919e5dd74687597), the answer should be $ \frac{1}{2450}$ which presumably comes from $\frac{1}{50}\times \frac{1}{49}$. But it seems that the order does not count. I did not assume that Alfonso got ticket $14$ first *then* Colin got ticket $23$ second.

Update: What is wrong with this reasoning.
When I said that I did not assume order, I meant that it's possible

* Alfonso got ticket $14$ first, then Colin got ticket $23$,
* Colin got ticket $23$ first, then Alfonso got ticket $14$.

Both of these possibilities are possible before the tickets are given out, so we can make an 'or' statement.
Label the event Alfonso got ticket $14$ by $A\_{14} $ and Colin got ticket $23$ by $A\_{23}$. Then by the addition rule

$ \Pr(\text{ ($A\_{14}$ first and $C\_{23}$ second) or ($C\_{23}$ first and $A\_{14}$ second}) ) 
\\ = \Pr(A\_{14}) \times \Pr(C\_{23} \mid A\_{14}) + \Pr(C\_{23}) \times \Pr(A\_{14}\mid C\_{23}) = \frac 1 {50} \times \frac 1 {49} \times 2.$

I realize that once the tickets are sold, then only one of $ \{ A\_{14}C\_{23}~ , ~ C\_{23}A\_{14} \}$ must occur, but before the tickets are sold both possibilities are plausible. Why would the probability change before and after the tickets are sold.