Arithmetic 20153

The teacher has 12 examples from geometry and 15 examples from arithmetic. How many papers can he create if he wants three examples from geometry and five from arithmetic in the letter?

Correct answer:

n =  660660

Step-by-step explanation:

$$\begin{gathered} C_3(12)=\left(\genfrac{}{}{0ex}{}{12}{3}\right)=\frac{12!}{3!(12-3)!}=\frac{12\cdot 11\cdot 10}{3\cdot 2\cdot 1}=220 \\ {C}_5(15)=\left(\genfrac{}{}{0ex}{}{15}{5}\right)=\frac{15!}{5!(15-5)!}=\frac{15\cdot 14\cdot 13\cdot 12\cdot 11}{5\cdot 4\cdot 3\cdot 2\cdot 1}=3003 \\ n=\left(\genfrac{}{}{0ex}{}{12}{3}\right)\cdot \left(\genfrac{}{}{0ex}{}{15}{5}\right)=220\cdot 3003=660660 \end{gathered}$$

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