Randolph Quirk -- A Comprehensive Grammar of the English Language  Sect. 6.9

Everyone thinks he has a right to be here.  <formal>
Has anybody brought his or her racket?
Has anybody brought their racket? <informal>

用 they 不算错，不过是 informal； 用 he 更正式；  用 he or she 亦可，特别是现在女权运动。
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