A teacher assigns a group of 30 students into 3 groups of 10. The way the assignment process works is as follows: the teacher first randomly picks 10 students from the class and assigns them to group 1; from the remaining group of students that have not been assigned, the teacher randomly picks 10 more and assigns them to group 2; finally, the remaining students not yet picked are all assigned to group 3.Henry and Marcel are friends and desperately want to be in the same group. To improve their chances, they quickly hide behind a cabinet, unnoticed, just before the teacher starts picking students. Immediately after the teacher has picked the 12thstudent, Henry quietly returns to his seat. Immediately after the teacher has picked the 16thstudent Marcel quietly returns to his seat. What is the probability that Henry and Marcel will be selected for the same group, and did they in fact improve their odds compared to simply staying in their seats the entire time?
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