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jmc

counting and probability intermediate

Problem

In how many ways can we seat 6 people at a round table if John and Sam insist on sitting next to each other? (Two seatings are equivalent if one is a rotation of the other.)
Solution
To take care of rotations, we can fix John at the topmost seat. We then have two choices for Sam: either side of John. The other four may sit anywhere in the other four seats. Thus there are ways.
Final answer
48