Which sentence is grammatically correct?

The selected sentence "Somebody left his or her jacket on the train" is grammatically correct because it properly matches a singular indefinite pronoun with its corresponding singular pronouns for possession. "Somebody" is considered a singular noun and therefore requires the use of "his or her" to maintain agreement in number. This structure clarifies that the jacket belongs to the unspecified individual referred to as "somebody."

In contrast, the other sentences do not consistently adhere to grammatical conventions. For example, using "Several" in the first choice incorrectly pairs a plural concept with singular pronouns, leading to confusion about ownership. The use of "everyone" in the second and third choices is typically treated as singular in American English, which generally leads to the use of singular pronouns like "his or her" instead of the plural "their." However, contemporary usage increasingly accepts "their" as a singular pronoun in informal contexts, though it may not be considered formal standard in all instances. The fourth option maintains the appropriate singular form, thus presenting a clear and correct construction.