Question

If from a pack four cards are drawn, find the chance that they will be the four honours of the same suit.

Answer 1

Honours of same suit means five highest card of each suit

Number of ways of drawing four cards $=$ ${}^{52}{C}_4$

Now we have to select one suit and four cards of that suit

So number of favourable outcomes $=$ ${}^4{C}_1{\times }^5{C}_4$

$\therefore$ required probability $=\frac{{}^4{C}_1{\times }^5{C}_4}{{}^{52}{C}_4}=\frac{20}{265200}=\frac{1}{13260}$