Topic probability

There are eight styles of graduation topics in the Slovak language. The Minister of Education draws 4 of them. How likely is he to choose at least one of the pairs?

Final Answer:

p =  40 %

Step-by-step explanation:

$$\begin{gathered} C_4(8)=\left(\genfrac{}{}{0ex}{}{8}{4}\right)=\frac{8!}{4!(8-4)!}=\frac{8\cdot 7\cdot 6\cdot 5}{4\cdot 3\cdot 2\cdot 1}=70 \\ t=\left(\genfrac{}{}{0ex}{}{8}{4}\right)=70 \\ {C}_2(8)=\left(\genfrac{}{}{0ex}{}{8}{2}\right)=\frac{8!}{2!(8-2)!}=\frac{8\cdot 7}{2\cdot 1}=28 \\ a=\left(\genfrac{}{}{0ex}{}{8}{2}\right)=28 \\ p=100\cdot a/t=100\cdot 28/70=40\% \end{gathered}$$

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