Question

Two cards are drawn at random from a pack of 52 cards. What is the probability that both the drawn cards are aces ?

Answer 1

Let S be the sample space. Then,

n(S) = number of ways of selecting 2 cards out of 52.

${=}^{52}{C}_2=\frac{(52\times 51)}{(2\times 1)}=1326$

Let E = event that both the cards drawn are aces. Then,

n(E) = number of ways of drawing 2 aces out of 4.

${=}^4{C}_2=\frac{(4\times 3)}{(2\times 1)}=6$

$P\left(getting2aces\right)=P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{6}{1326}=\frac{1}{221}$