Here's a little question that I'm trying to solve:
There are k students standing in a line. What's the number of permutation if John is standing left to Jack?
Here's my attempt: $\sum_{i=2}^{k} \sum_{j=1}^{i-1}(k-2)!$ Jack is in the i'th index and John is in the j'th index. The are k-2 people left.
I don't see a mistake here, but it feels to complicated. Also with combinatorics I never know if I'm right or not.
Any comments? Thanks!