Question

From a deck of 52 cards, four cards arc drawn simultaneously, find the chance that they will be the four honours of the same suit.

Answer 1

Since from a deck of cards, four cards are drawn
$\therefore n\left(S\right){=}^{52}{C}_4$

Let E be the event of that all the four cards drawn are honour cards from saint suit.

[$\because$ Honour cards means king, queen, jack and ace]

$\therefore E{=}^4{C}_{4}o{r}^4{C}_{4}o{r}^4{C}_{4}o{r}^4{C}_4\Rightarrow n\left(E\right)=4{\times }^4{C}_4=4$

$\therefore P\left(3\right)=\frac{4}{{}^{52}{C}_4}=\frac{4!}{\frac{52!}{4!\times 48!}}=\frac{4!\times 4\times 48!}{52!}$

$=\frac{4\times 4\times 3\times 2\times 1}{52\times 51\times 50\times 49}=\frac{96}{6497400}$

$=\frac{4}{270725}$