The card game Cribbage uses a standard 52 card deck. Each player is dealt 4 cards, and the order doesnt matter. How many different 4 card hands are possible?
The number of combinations of 4 card from the set of 52 cards is,
$\begin{array}{rcl}n& =& {}^{52}C_{4}\\ & =& \frac{52\times 51\times 50\times 49}{4\times 3\times 2\times 1}\\ & =& 270725\end{array}$
Thus, there 270725 such 4 card hands are possible.