My program gives 322560/39916800 = 0.008 08 ...
[Execution time = 11.3s, for the curious.]
I am having trouble producing the same via math. 🙂
My only curiosity is where do you get your programme from?
If you have made it yourself well done.
I would like a copy!
I also got some enormous numbers when I tried the combinations method.
As to the answer,I expect you're correct as usual.
I tried it a different way but got bogged down (as usual!!)
There are 4 distinct groups AA EE PP and YTRSH
It doesn't matter how they are arranged within the groups or where the groups appear in the complete sequence.
So 3/4 = .75
Then we come to if the pairs AA EE PP are split.
Not having a programme!,I tried it "longhand" first for the A's split and the EE and PP together.
I concluded that the A's could occupy 25 positions in the sequence (positions 1,3 1,4 etc through to 5,9)EE PP A
for 3 ,9 for example.
I then got to wondering if this could be applied similarly to the E's and P's so the answer could be (3/4 )/(9/25)*3 or something.
This will be wrong, but it all helps to keep ones mind active!!