# Hangout Rearrangements

**Discrete Mathematics**Level 4

Calvin was running a Master Session about combinatorics using Brilliant hangouts. The pictures of all the students enrolled in the session were shown in a line at the bottom of the screen. Christian, a student in the class, made the following comment: "There are at least 9 students in this session. If you count the number of ways that the pictures can be arranged so that my picture is next to Mehrnoush's picture, it is the same as the number of ways that the pictures can be arranged so that there are either 7 or 8 pictures between my picture and Mehrnoush's picture." If what Christian said is true, how many students were enrolled in the Master Session?

**Details and assumptions**

Only the student's pictures appear at the bottom of the screen. Calvin's picture (and presentation notes) does not appear at the bottom of the screen.

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