1. **State the problem:** We have 850 elephants in total. \n\n2. **Identify the given information:** \n- 1/5 of the elephants are Asian elephants. \n- 40% of the Asian elephants are male. \n\n3. **Find the number of Asian elephants:** \n$$\text{Asian elephants} = \frac{1}{5} \times 850 = 170$$ \n\n4. **Calculate the number of male Asian elephants:** \n$$\text{Male Asian elephants} = 40\% \times 170 = 0.40 \times 170 = 68$$ \n\n5. **Calculate the number of female Asian elephants:** \nSince the total Asian elephants are 170 and 68 are male, the rest are female. \n$$\text{Female Asian elephants} = 170 - 68 = 102$$ \n\n**Final answer:** There are **102 female Asian elephants**.