How can one reconcile the prohibition of mixing (between genders) in Islamic law with the jurisprudential principle that states, "What is prohibited to block a means (to sin) is permissible in cases of need," especially when there is a desire to pursue postgraduate studies in a mixed environment to secure a livelihood, given that mixing has previously led to deviation?

That which is prohibited as a means to prevent an evil (sadd al-dhari'ah) may be permitted for an overriding benefit (maslahah rajihah), such as an urgent need that approaches necessity, due to the hardship and difficulty that would result from its absence. In such cases, it takes the place of necessity or entails a benefit that outweighs the harm. However, seeking employment and increasing income is not considered a necessity or an urgent need that permits intermingling (ikhtilat), as these can be obtained through lawful means.