Three students are each given one letter. nobody has the same letter. each student can only see his/her own letter and are told that their letters only spell one of the following words:

pet, can, new, tap, pry, pen

they are asked the question "do you know which word can be spelled by your letters? " three times. they all answer at the same time and can hear the other students' answers.

first time: all answer 'no.'
second time: all answer 'no.'
third time: all answer 'yes.'

what word do their letters spell? explain.