<s>[INST] Combination and product question There are $5$ numbers, and each combination of $4$ numbers from those $5$ has a product of either $10, 20, 30, 40$, or $50$. What is the quotient of the sum of those $5$ numbers divided by the product of all $5$ numbers?
 [/INST] The sum of these number divided by their product is:
$$
   \frac{m_1+m_2+m_3+m_4+m_5}{m_1 m_2 m_3 m_4 m_5} = \frac{1}{m_2 m_3 m_4 m_5} + \frac{1}{m_1  m_3 m_4 m_5} + \frac{1}{m_1 m_2 m_4 m_5} +  \frac{1}{m_1 m_2 m_3 m_5} +  \frac{1}{m_1 m_2 m_3 m_4} = \frac{1}{10} + \frac{1}{20} + \frac{1}{30} + \frac{1}{40} + \frac{1}{50} = \frac{137}{600} \approx 0.228333
$$
</s>