Compute the number of a 5-card poker hands containing four 10s

5-card-poker-hands

#1

compute the number of a 5-card poker hands containing four 10s.

d) Compute the number of a 5-card poker hands containing any “four of a kind”. Hint: think, how many kinds are in the standard 52-card deck.

e) Three of a kind and a pair is a poker hand, that contains three cards of one rank and two cards of another (unmatched) rank. Compute the number of a 5-card poker hands containing three Aces and two Kings.

(f) Compute the number of a 5-card poker hands containing three 2s and two 3s.

g) Compute the number of a 5-card poker hands containing any “three of a kind and a pair”.

h) Compute the number of a 5-card poker hands containing 2 red Aces, 2 black Kings, and 1 red queen.

i) Compute the number of a 5-card poker hands containing 2 any Aces, 2 any Kings, and 1 any queen.

Answer:

the number of a 5-card poker hands containing four 10s : 52-4=48
d) 4813=624
e) 4C3
4C2=24
f) 24
g) 131224=3744
h) 2C22C22C1=2
i) 4C24C24C1=144