Question

From a pack of 52 cards, four cards are drawn. The chance that they will be the four honours of the same suit is $k/541450$. Find the value of $k$.

Answer 1

Here $n$= Total no. of ways $m$=${}^{52}{C}_4$= $\frac{52\times 51\times 50\times 49}{1\times 2\times 3\times 4}=13\times 17\times 25\times 49=270725.$
There are four honours (ace,king,queen and knave)in each suit and so there are $4$ sets of $4$ honours each.
To obtain the favourable number of ways, we have to select one suit of four honours from these four sets.
$\therefore m={}^4{C}_1=4$
$\therefore p=$required probability $=\frac{m}{n}=\frac{4}{270725}$

Comparing with $\frac{k}{541450}$, we get the value of $k=8$