Ten persons

Ten persons, each person makes a hand to each person. How many hands were given?

Correct answer:

x =  45

Step-by-step explanation:

$$\begin{gathered} C_2(10)=\left({\displaystyle \genfrac{}{}{0px}{}{10}{2}}\right)={\displaystyle \frac{10!}{2!(10-2)!}}={\displaystyle \frac{10\cdot 9}{2\cdot 1}}=45 \\ n=10 \\ x=\left(\genfrac{}{}{0px}{}{n}{2}\right)=45 \end{gathered}$$

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