这道选择题不够严谨

有一读者问： 有这样一道选择题：

The teacher entered the classroom, _____.

A. with book in hand　B. a book in hand

C. with a book in his hand　D. book in his hand

答案是A，但我觉得应选C，请解答。

这道选择题不够严谨。可选A，亦可选B；亦可选C，但其前最好无逗号。顺便提一下，此题还可填以 book in hand， 虽较文气。