I need some help for my school project that I'm currently working on.
Let's say you have 26 ports, and N wires. With a wire you can connect 2 ports (duh )
When you have only 1 wire, you can make 26C2=325 possible combinations (not 26*25 because A-B = B-A). But how many combinations can you make with 2 wires? And with 6 and 10?
With 2 wires, I thought 44850 but my teacher said 89700. Which one is true?
I'm 99% sure that with 10 wires you can make 150*10^12 combinations.
Also, you can use a port only once.

Thanks

You're looking for the multinomial coefficient. That gives the number of ways N objects can be divided into distinguishable groups (where order within a group does not matter) of size n1, n2, n3, ... where Σn = N.

It is calculated as:



So, with 2 wires you are splitting the 26 ports in groups of 2, 2, and 22. This is equal to


Code:


However, due to order of the groups not mattering, you need to divide by 2! (2 is the number of groups of 2) again, so the answer is 44850.