Hello MathStackExchange Community,
Confused about how to change the notation-formula for permutations when you have more complex processes. i.e. multiple independent action choices of different types of objects and orientation limitations.
- The generic formula is : $P(n,r)= n!/(n-r)!$
- $n!$ = being the total number of objects in an option set
- $(n-r)!$ = the limitations caused by the choices made.
but this only works for very simple permutation-processes where you make one single choice-type.
If I have 15 particles, 10 neutral and 5 positive particles and I care about the arrangement
he formula is $P(n,r)= 15!/10!\cdot5!$
What I don't get is how does 10! 5! translate to $(n-r)!$
the second part of the problem asks, if like charges repel, and positive charges can't sit next to each other- number of possibilities then?
What is the way to think about the second portion? Could draw it out and try to find a pattern, but if I had avagadro's number of particles that would be hard.