2008 iTest Problems/Problem 67
Revision as of 21:02, 7 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 67 — circular seating charts)
Problem
At lunch, the seven members of the Kubik family sits down to eat lunch together at a round table. In how many distinct ways can the family sit at the table if Alexis refuses to sit next to Joshua? (Two arrangements are not considered distinct if one is a rotation of the other.)
Solution
Let Alexis sit at a designated spot, which "pins" the circle and prevents any cases from being overcounted due to symmetry. Joshua has 
spots to choose from since he can not sit next to Alexis. The remaining five members can sit anywhere, so there are 
distinct ways for the family to sit at the table.
See Also
| 2008 iTest (Problems) | ||
| Preceded by: Problem 66 |
Followed by: Problem 68 | |
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