。
She was chosen out of ten thousand applicants.
Literal
She [topic-は] ten-thousand-people [genitive-の] applicants [genitive-の] inside-from chosen-was.
選ばれた is the passive of 選ぶ ('to choose'); for godan verbs the passive is formed with ~れる, here in past form. の中から ('from among / out of') is a compound particle frame: 中 ('inside') marks the relevant set, から ('from') the source of selection. 一万人の応募者 puts a quantity (一万人, ten thousand people) before の to specify the noun ('ten thousand applicants'). The people-counter 人 reads にん for groups of three or more; for one or two it takes the native readings ひとり and ふたり.