Question

You pick 5 cards from a 52 card deck, find the probability of all spades, a flush (all the same suite) and four of a kind (4 cards of the same value). Remember there are five cards picked, so 4 have the same value and then there is a fifth card.

Answer 1

P(all spades)=13/52

Answer 2

\[P(all\ spades)=\frac{\left(\begin{matrix}13 \\ 5\end{matrix}\right)}{\left(\begin{matrix}52 \\ 5\end{matrix}\right)}=\frac{13!}{5!8!}\times\frac{5!47!}{52!}\]

Answer 3

The probability of all spades is given by:
(number of combinations of the 13 spades taken 5 at a time) divided by (number of combinations of the 52 cards in the pack taken 5 at a time)
\[\frac{13!}{5!8!}\times\frac{5!47!}{52!}=\frac{13\times12\times11\times10\times9}{52\times51\times50\times49\times48}=you\ can\ calculate\]

Answer 4

@kropot72

A little \(\LaTeX\) tip for you. If you want something like 13 choose 5 then try using

{13 \choose 5}

\[{13\choose 5}\]

or \binom{13}{5}

\[\binom{13}{5}\]

it is less work :)

Answer 5

so that would be 1287?

Answer 6

@weto
\[P(all\ spades)=\frac{154440}{311875200}=0.0005\]

Answer 7

@Zarkon Many thanks. I'll use it :)