Seven cards are dealt at random from a regular deck of 52 playing cards. Find the probability that exactly 4 are spades. Round your answer to four decimal places.
+118613 48C3 / 52C7
$${\frac{{\left({\frac{{\mathtt{48}}{!}}{{\mathtt{3}}{!}{\mathtt{\,\times\,}}({\mathtt{48}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)}}{{\left({\frac{{\mathtt{52}}{!}}{{\mathtt{7}}{!}{\mathtt{\,\times\,}}({\mathtt{52}}{\mathtt{\,-\,}}{\mathtt{7}}){!}}}\right)}}} = {\frac{{\mathtt{1}}}{{\mathtt{7\,735}}}} = {\mathtt{0.000\: \!129\: \!282\: \!482\: \!223\: \!7}}$$
i think that is right :/
+118613 48C3 / 52C7
$${\frac{{\left({\frac{{\mathtt{48}}{!}}{{\mathtt{3}}{!}{\mathtt{\,\times\,}}({\mathtt{48}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)}}{{\left({\frac{{\mathtt{52}}{!}}{{\mathtt{7}}{!}{\mathtt{\,\times\,}}({\mathtt{52}}{\mathtt{\,-\,}}{\mathtt{7}}){!}}}\right)}}} = {\frac{{\mathtt{1}}}{{\mathtt{7\,735}}}} = {\mathtt{0.000\: \!129\: \!282\: \!482\: \!223\: \!7}}$$
i think that is right :/
