Each person has his own way ... Each person has his or her own way ... Each person has her 1 own way ... Each person has their own way ... When I was young, Each person has his ... was common. Then, the preferred usage changed to Each person has his or her ... and later Each person has her 1.... Nowadays, singular they is also acceptable. More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.