Card drawing probability

Determine the probability that when drawing three cards from a complete set of 32 marriage cards, it will be the same acorns or the kings themselves.

Final Answer:

p =  0.0016

Step-by-step explanation:

$$\begin{gathered} C_3(32)=\left(\genfrac{}{}{0ex}{}{32}{3}\right)=\frac{32!}{3!(32-3)!}=\frac{32\cdot 31\cdot 30}{3\cdot 2\cdot 1}=4960 \\ n=32 \\ {n}_1=\left(\genfrac{}{}{0ex}{}{n}{3}\right)=4960 \\ {C}_3(4)=\left(\genfrac{}{}{0ex}{}{4}{3}\right)=\frac{4!}{3!(4-3)!}=\frac{4}{1}=4 \\ {n}_2=\left(\genfrac{}{}{0ex}{}{4}{3}\right)=4 \\ p=\frac{2\cdot n_2}{n_1}=\frac{2\cdot 4}{4960}=\frac{1}{620}=0.0016 \end{gathered}$$

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