A pronoun must agree in gender and number with its antecedent. If necessary, vary your choice of pronouns to avoid sexist language. Sometimes the best way to avoid sexist language is to change the singular to the plural.
In the United States, an astronaut candidate must be
recommended by their previous organization.
In the United States, an astronaut candidate must be
recommended by his previous organization.
In the United States, an astronaut candidate must be
recommended by her previous organization.
In the United States, astronaut candidates must be
recommended by their previous organizations.
--"Astronaut Selection and Training," Compton's Encyclopedia (modified)
When the antecedent is a singular indefinite pronoun, use a singular pronoun to refer to it. In such cases, vary your choice of pronouns to avoid sexist language. Sometimes the best way to avoid sexist language is to change the singular to the plural.
Each of the astronaut candidates sent
their photograph with their
application.
Each of the astronaut candidates sent
his photograph with his application.
Each of the astronaut candidates sent
her photograph with her application.
All of the astronauts sent their
photographs with their applications.
When the antecedent is a plural indefinite pronoun, use a plural pronoun to refer to it.
Some of the astronaut candidates sent
his photograph with his application.
Some of the astronaut candidates sent
her photograph with her application.
Some of the astronaut candidates sent
their photographs with their
applications.
Use a plural pronoun to refer to antecedents joined by the coordinating conjunction and.
The ceramic tile and the aluminum alloy used in the
experiment retained its initial hardness.
The ceramic tile and the aluminum alloy used in the
experiment retained their initial hardness.
Use a pronoun that agrees in gender and number with the closest antecedent to refer to antecedents joined by the coordinating conjunctions or and nor.
Either the disks or the motor need
their parts repositioned.
Either the disks or the motor needs
its parts repositioned.
Either the motor or the disks need
their parts repositioned.
Use a singular pronoun to refer to antecedents preceded by each or every.
Each ceramic tile and aluminum alloy sample used in the
experiment retained their initial hardness.
Each ceramic tile and aluminum alloy sample used in the
experiment retained its initial hardness.
Special case: If each follows a plural antecedent, use a plural pronoun.
They each sent in his application.
Tom and Jerry each sent in his
application.
They each sent in their applications.
Tom and Jerry each sent in their
applications.
Use a singular pronoun to refer to a collective noun acting as a group.
The astronaut selection committee submits
their decision to NASA.
The astronaut selection committee submits
its decision to NASA.
Use a plural pronoun to refer to the members of a collective noun acting as individuals.
The astronaut selection committee vote for
its favorite candidates.
The astronaut selection committee vote for
their favorite candidates.
The members of the astronout selection committee vote
for their favorite candidates.
