In talking to a student, I realized I didn't make something clear in describing the rand-index based external cluster evaluation method.
Rand-Index classifies every pair of entities e1,e2 into four categories
[in-the-same-ground-truth-cluster, in-the-same-generated-cluster] A
[in-the-same-ground-truth-cluster, in-different-generated-clusters] C
[in-different-ground-truth-clusters, in-the-same-generated-cluster] B
[in-different-ground-truth-clusters, in-different-generated-clusters] D
If A,B,C,D are the number in each class, then A+B+C+D will be n*(n-1)/2 (which is the number of pairs over n entities).
I modified the slide to make this point clear..