Problem
The Problem
A standard 52-card deck is dealt into 5-card poker hands. Compute the probability of each:
- Royal flush (A-K-Q-J-10 all same suit).
- Straight flush (5 consecutive same suit, not royal).
- Four of a kind.
- Full house (3 of one rank + 2 of another).
- Flush (5 same suit, not straight flush).
- Straight (5 consecutive ranks, not flush).
- Two pairs.
Express all answers as exact fractions, then rank by probability (which is most common?).