A professor knows $9$ jokes and tells $3$ jokes per lecture. Prove that in a course of $13$ lectures there is going to be a pair of jokes that will be told together in at least $2$ lectures.

I've started with counting how many possibilities there are to tell jokes in a lecture. Let

$$J := \{1,2,\dots,9\}$$

The amount of all different possible combinations for jokes is $9 \choose 3$ and for each lecture there are going to be $3$ unique pairs of jokes $\left(\frac{3!}{2!}=3\right)$.

I'm not sure how to continue from here to get to the PHP, I think I might be doing something wrong here, any advice how to abstract it properly?

This is an exercise from the Tel-Aviv University entry test preparation and I'm not a student yet so elementry combinatorics should do here.