Question

Say we have 25 nodes in a graph. In how many ways can we split the graph into two subsets with 12 nodes in one and 13 in the other?

Answer 1

The number of ways to split a graph with 25 nodes into two subsets with 12 nodes in one and 13 in the other can be calculated using combinations formula.

Step-by-step explanation:

The number of ways to split a graph with 25 nodes into two subsets with 12 nodes in one and 13 in the other can be calculated using combinations. In this case, we need to choose 12 nodes out of 25 to form one subset, and the rest will form the other subset. The formula for combinations is given by C(n, k) = n! / (k!(n-k)!).

Using this formula, we can calculate the number of ways as follows:

C(25, 12) = 25! / (12!(25-12)!) = 25! / (12!13!)

Simplifying this expression gives us the final answer.