What are the odds that after hitting shuffle twice on a 155 unique songs playlist on spotify, 3 of the 6 first songs are the same on both shuffle. Imagine you have $155$ unique songs in a playlist on Spotify. You hit shuffle. Out of the first $6$ songs, you have $3$ particular songs that we'll name "song A", "song B", and "song C". The order in which these $3$ songs show up within those first $6$ songs doesn't matter. Then, you hit shuffle again and get another set of $6$ songs. $3$ of those $6$ songs are once again A, B, and C. What are the odds of this happening?
I'm kinda stuck trying to math this. I know that you have
$$\frac{155!}{6!(155-6)!}$$
different ways to select $6$ songs and that would be a denominator for a probability "P". You would then get a numerator and multiply $P$ by itself ($P^2$) because we shuffle $2$ times. Anyways, I think that's what I need to do. The numerator is where I get stuck. Not sure how to calculate it. Anyone can help? Am I on the right track?

My understanding of the problem is that the first selections are just random and designating A, B, C is after the first round.
The probability that these 3 of the 6 songs are repeated is $\binom{6}{3}\frac {3\times 2\times 1}{155\times 154\times 153}$.  The binomial factor represents the fact that the order of selection doesn't matter.
