What principle states that during gamete formation genes for different traits separate without influencing each other's inheritance?

The correct answer is the principle of independent assortment.

According to the principle of independent assortment, at the time of gamete formation genes for distinct traits separate without affecting the inheritance of each other. This law was postulated by Gregor Mendel. According to Mendel, when two or more characteristics are inherited, the individual hereditary factors assort independently at the time of gamete formation, providing different traits an equal chance of occurring together.