Do you support or frown upon the use of the singular 'they/their'? Should it not be used in formal correspondence? The use of 'he/she,' 'his/her' can become annoyingly cumbersome and unwieldy. Without rewording, would you frown upon these? Everyone at the meeting said they felt uncomfortable with the new CEO. Everybody was upset with their choices. Everyone returned to their seats. Somebody left their camera in the lobby. Thanks.
I was torn about this usage until I learned that it's a very old usage--the prohibition of the singular "they" and the insistence on the generic "he" is relatively recent. (Where "relatively" is measured in centuries--it's less than two hundred years old.) Now I'm entirely in its favor, though that doesn't necessarily mean that I would use it in situations where someone's judgement of the correctness of my writing would have substantial consequences.
Although 'somebody' is singular and 'their' is plural, I think they sound good together. 'Somebody left their camera in the lobby' sounds better than 'Somebody left his or her camera in the lobby.' There's no disputing this, IMO.
More and more people are using the singular they, and I actually think it's considered accepted usage by some style guides. I don't mind when people use it. I sometimes use it myself, though I tend to use "he" instead.
I would use 'he' or 'his' when the unidentified subject is singular. It sounds wrong to me otherwise. Before I'm accused (again) of misogyny, my solution to the his/her thing is for the speaker or writer use his or her own gender. I would say, "A good plumber is worth his weight in gold." My sister would write, "A good plumber is worth her weight in gold." Since there are roughly as many men as women, it would average out.