Indicator Variables: The Swiss Army Knife of Expectation

(a) In a random permutation of $\{1, 2, \ldots, n\}$, what is the expected number of elements in their "correct" position (fixed points)? (b) At a party of $n$ people, each person shakes hands with every other person. Then each person independently forgets each handshake with probability $1\mathrm{/}2$$\frac{1}{2}$. What is the expected number of pairs where exactly one person remembers the handshake? (c) You deal a standard 52-card deck. What is the expected number of times an Ace appears directly before a King?