How many 5-card poker hands contain four "10"s.a) How many 5-card poker hands contain any "four of a kind".?

Aneeka Hunt

Aneeka Hunt

Answered question

2021-09-08

How many 5-card poker hands contain four "10"s.
a) How many 5-card poker hands contain any "four of a kind".?
b) How many 5-card poker hand combinations contain aces full of kings (3×A+2×K).
c) How many 5-card poker hand combinations contain a full house.
d) How many 5-card poker hand combinations contain 2 red Aces, 2 black Kings, and 1 red queen.
f) How many 5-card poker hand combinations contain 2 Aces, 2 Kings, and 1 queen.

Answer & Explanation

Obiajulu

Obiajulu

Skilled2021-09-09Added 98 answers

a) Four tens (always) + any card
Since only the last card will change with each variation, there're
52-4=48
hands with 4 tens.
b) There're 4 combinations of AAA and 6 combinations of KK. So there are
4xx6=24
hands with aces full kings
c) Same as the previous, except it could be any card of the 13 for the "3 of a kind" and any card of the remaining 12 for the "pair". So, there are
24×13×12=3744
hands with a full house
d) There's one combination of red aces, 1 combination of black kings, and 2 single red queens, so there're
1×1×2=2
hands with all of them
e) There're 6 combinations of aces "pairs", 6 for kings, and 4 single queens. So there're
6×6×4=144
hands with all of them.

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