APT ..... in other words Anne before Pela before Tony
PAT ..... which is Pela before Anne before Tony.
Those are the 2 possible orderings of the 3.
Now to find the number of ways we have APT in the 7,
we only need select 3 positions of the 7,
so we count the number of ways we can do that.
A before P before T occurs in ways.
The same calculation counts the number of ways Pela is before Anne who is before Tony.
Having counted the number of ways we can have APT,
there are 4! ways to arrange the remaining 4 people each time.
This will help to find the numerator of the probability fraction.
Needless to say, there are sure to be quicker ways.
For example, you may ask...
Is it just as likely that Tony will be in front of Pela and Anne,
in between Pela and Anne,
or behind Pela and Anne.