Question

What is the theoretical probability of being dealt exactly three 4's in a 5-card hand from a standard 52-card deck

Answer 1

# of ways to get 3 4's: 4C3 = 4
---
# of ways to get 2 non-3 cards: 48C3 = 17296
----
# of ways to get 3 4's and 2 other = 4*17296

------
# of ways to get 5 cards randomly: 52C5
=============================================
P(3 4's and 2 other) = (4*17296)/52C5 = 0.0266

Answer 2

Your answer would be something like 94/54145