Find the probability of drawing an ace and a black queen together from a well shuffled deck of cards.

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{When} \mathrm{two} \mathrm{cards} \mathrm{are} \mathrm{dran} \mathrm{from} \mathrm{a} \mathrm{pack} \mathrm{of} 52 \mathrm{cards}. \\ \mathrm{Total} \mathrm{no}. \mathrm{of} \mathrm{exhaustive} \mathrm{cases}={}^{52}\mathrm{C}_2 \\ =\frac{52!}{2!\left(52-2\right)!} \\ =\frac{52\times 51}{2} \\ =26\times 51 \\ \mathrm{Let} \mathrm{A} \mathrm{be} \mathrm{the} \mathrm{event} \mathrm{of} \mathrm{getting} \mathrm{an} \mathrm{ace} \mathrm{and} \mathrm{a} \mathrm{black} \mathrm{queen}. \\ \mathrm{A}={}^4\mathrm{C}_1\times {}^2\mathrm{C}_1 \\ =\frac{4!}{1!\left(4-1\right)!}\times \frac{2!}{1!\left(2-1\right)!} \\ =4\times 2 \\ =8 \\ \mathrm{Thus}, \\ \mathrm{P}\left(\mathrm{A}\right)=\frac{8}{26\times 51}=\frac{\mathbf{4}}{\mathbf{663}} \end{gathered}$$
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