Question

what is the theoretical probability of being dealt all four 7's ina 5 card hand?

Answer 1

Are you familiar with the combination formula?

Answer 2

probability = (possible hands with four 7's)/ (all possible hands)

total num of hands = 52 choose 5

num of hands w/ four 7's = (4 choose 4)*(48 choose 1)

\[P = \frac{\left(\begin{matrix}4 \\ 4\end{matrix}\right)*\left(\begin{matrix}48 \\ 1\end{matrix}\right)}{\left(\begin{matrix}52 \\ 5\end{matrix}\right)}\]
formula for combinations
\[\left(\begin{matrix}n \\ k\end{matrix}\right) = \frac{n!}{k! (n-k)!}\]