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?
 A: The sum of these number divided by their product is:
$$
   \frac{m_1+m_2+m_3+m_4+m_5}{m_1 m_2 m_3 m_4 m_5} = \frac{1}{m_2 m_3 m_4 m_5} + \frac{1}{m_1  m_3 m_4 m_5} + \frac{1}{m_1 m_2 m_4 m_5} +  \frac{1}{m_1 m_2 m_3 m_5} +  \frac{1}{m_1 m_2 m_3 m_4} = \frac{1}{10} + \frac{1}{20} + \frac{1}{30} + \frac{1}{40} + \frac{1}{50} = \frac{137}{600} \approx 0.228333
$$
A: Assuming you mean that each combination of $4$ has a different product (so all of $10,20,30,40,$ and $50$) are used, the product of all the numbers is $p=12000000^{\frac 14} \approx 58.5866$ and we have $10=\frac p{n_1},$ etc.  Then $$n_1=\frac p{10}\approx 5.85866\\n_2=\frac p{20} \approx 2.94283\\n_3=\frac p{30}\approx 1.96189\\n_4=\frac p{40}\approx 1.471415\\n_5=\frac p{50}\approx 1.177132$$  and the sum of all divided by the product is about $$0.228333$$
Alternately, if the products are chosen from that set but repetition is allowed, all the numbers can be equal and can be any one of $10^{\frac 14},20^{\frac 14},30^{\frac 14},40^{\frac 14},50^{\frac 14},$ and in these cases the sum divided by the product is $$\frac 12,\frac 14, \frac 16, \frac 18, \frac 1{10}$$
