Problem 168
easy
Five cards of one suit
How many 5-card hands from a standard 52-card deck have all five cards of the same suit? Straight flushes count too.
Answer
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Hints 0/2
Pick the suit, then pick five cards from it.
Each suit has 13 cards.
h
Solution
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. A one-suit hand is a choice of suit followed by a choice of 5 of its 13 cards.
Step 1. There are 4 suits.
Step 2. Each suit gives hands.
Step 3.
In poker. A “flush” in poker excludes the 40 straight flushes (10 per suit), which leaves 5108. The probability of being dealt five cards of one suit is .