Answer to Question #260293 in Statistics and Probability for Ecem

Question

In a poker hand consisting of 5​ cards, find the probability of holding​ (a) 3 kings​; ​(b) 4 red cards and 1 club.

Answer 1

for 52 card deck:

a)

$P=\frac{4}{52}\cdot \frac{3}{51}\cdot \frac{2}{50}\cdot \frac{48}{49}\cdot \frac{47}{48}=\frac{47}{270725}$

b)

$P=\frac{1}{2}\cdot \frac{25}{51}\cdot \frac{24}{50}\cdot \frac{23}{49}\cdot \frac{13}{48}=\frac{299}{19992}$