Say I have k
students, four of them are Jack, Liz, Jenna and Tracy. I want to count the number of permutations in which Liz is standing left to Jack and Jenna is standing right to Tracy. I define $A = ${Liz is left to Jack} so $|A| = \frac{k!}{2}$. The same goes for $B$ with Jenna and Tracy.
I know that $|A \cap B| = |A| + |B| - |A \cup B|$
But how do I find the union? I'm guessing it involves inclusion-exclusion, but I can't remember how exactly.
Any ideas? Thanks!