To play a particular card game, each player is dealt five cards from a standard deck of 52 cards. How
many different hands are possible?
Given,
Each player is dealt five cards from a standard deck of 52 cards.
To find,
How many different hands are possible?
Answer:
Here we use commbination formula to find required different hands:
$\left(\begin{array}{c}n\\ r\end{array}\right)=\frac{n!}{r!(n-r)!}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\begin{array}{c}52\\ 5\end{array}\right)=\frac{52!}{5!(52-5)!}=2598960$
Therefore, 2598960 different hands are possible.