This is the 15104th most frequent Turkish word.
seçilmesinin
"The act of being chosen or elected."
The word 'seçilmesinin' is used as a noun formed from the verb 'seçmek' through the suffix '-il-' signifying passive voice, and '-mesi-' denoting a nominalized form with '-nin' case ending for possession or relation.
Başkanlık görevine onun seçilmesinin ülkede büyük bir değişimi başlatacağı düşünülüyordu.
It was thought that her election to the presidency would initiate a significant change in the country.
Here, 'seçilmesinin' serves as a nominalized action indicating possession or relation to Ali's being chosen, formed from the verb 'seçmek' as described before.
Matematik yarışmasında Ali'nin seçilmesinin herkesi çok şaşırttığı anlaşılıyor.
It becomes apparent that Ali's selection in the math competition surprised everyone greatly.
In this instance, 'seçilmesinin' is again indicating the act of Mehmet being chosen with surrounding context emphasizing its correctness, using similar linguistic constructions.