Probability of Ace and King of same suit and probability of quads

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Compute the probability that a hand of 13 cards contains (a) the Ace and King of at least one suit; (b) all 4 of at least 1 of the 13 denominations.

Below, you will see the work that I had for this problem, yet I was told is completely wrong. The solution used the inclusion-exclusion formula, was long and drawn out, and seemingly much over the scope of the class. The answers I got for both were within 0.01 of the answers provided. What was wrong with my answer?

Work for both parts of the problem