Everybody, Anybody.—Refers to male and female.
For want of a pronoun of common gender, use the masculine—he, his, him—unless the other sex is specified. “They” is plural and must not be used.
Anybody can do what they like. (wrong.)
Anybody can do what he likes.
Everybody will have to make up their minds. (wrong.)
Everybody will have to make up his mind.
Everybody has their faults. (wrong.)
Everybody has his faults.
If anybody calls, let them wait. (wrong.)
If anybody calls, let him wait.