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Have I correctly used 'it' and 'at hand' in my sentences?

Professor Lewis handed pieces of paper to his students and asked each of them to get a piece and pass the other pieces and write his/her favorite word on it and drop it into the box at hand. Then she called each of them to pick a piece of paper from the box, read and explain the word written on it, & tell about his/her expectations of him as his/her professor.

Context: In the sentences above, 'his/her' refer to 'each' of the students.

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Professor Lewis handed out pieces of paper to his students and asked each of them to take one. Then he asked each student to write his or her favorite word and drop it into the box at hand. Then he called on each of them to pick a piece of paper from the box, read it, explain the word written on it, and explain his or her expectations of him as his or her professor

I've assumed Lewis is a man.

Comments  

A million thanks to you, Clive.