How many different 5-card hands can be dealt from a standard 52-card deck?
I've highlighted the word different because I believe it's the key to the question, am I right in thinking the answer is
$\displaystyle 52*51*50*49*48 = 311,875,200$
How many different 5-card hands can be dealt from a standard 52-card deck?
I've highlighted the word different because I believe it's the key to the question, am I right in thinking the answer is
$\displaystyle 52*51*50*49*48 = 311,875,200$
No, they wouldn't. Your answer, 52*51*50*49*48, which is the same as $\displaystyle \frac{52!}{47!}$ or $\displaystyle _{52}P_5$ which includes the same cards in different orders. To not count the same cards in different orders as different hands, you need to divide by 5!, the number of orders of the same 5 cards. That will give you $\displaystyle \frac{52*51*50*49*48}{5!}$ which is exactly $\displaystyle \frac{52!}{5! 47!}= \begin{pmatrix}52 \\ 5\end{pmatrix}$ as Plato said.