In poker, a person is dealt 5 cards from a standard 52-card deck. The order in which you are dealt the 5 cards does not matter. How many different 5-card poker hands are possible?
Given:
A person is dealt 5 cards from a standard 52-card deck.
The objective is to find the different number of possible 5-card poker hands.
Let's find the different combinations.
${}^{n}C_{r}=\frac{n!}{(n-r)!r!}\phantom{\rule{0ex}{0ex}}{}^{52}C_{5}=\frac{52!}{(52-5)!5!}\phantom{\rule{0ex}{0ex}}{}^{52}C_{5}=\frac{52!}{47!5!}\phantom{\rule{0ex}{0ex}}{}^{52}C_{5}=\frac{52\times 51\times 50\times 49\times 48\times 47!}{47!\times 5\times 4\times 3\times 2\times 1}\phantom{\rule{0ex}{0ex}}{}^{52}C_{5}=52\times 51\times 5\times 49\times 4\phantom{\rule{0ex}{0ex}}{}^{52}C_{5}=2598960.$
Hence, the different number of possible 5-card poker hands are 2,598,960.