Anonymous

# Another Permutation Problem: You guys were so helpful last time - I have one more that is bothering me?

Another permutation problem: Ten people are seated at a rectangular table. Tanya will sit at the head of the table. Henry must not be seated beside either Wilson or Nancy. In how many ways can the people be seated. Answer: 201 600 Explanation anyone? Please and Thank You....I tried hard to get this one - no success....

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• kb
Lv 7

Use Inclusion-Exclusion. (Ignore Tanya; so there are 9 people to arrange.)

There are 9! ways to arrange the 9 people.

There are 2! * 8! ways to arrange the people so that Henry is next to Nancy (the 2! is from Henry, then Nancy or vice versa).

Likewise, there are 2! * 8! ways to arrange the people so that Henry is next to Wilson.

Finally, there are 2! * 7! ways to arrange the people so that Henry is between Nancy and Wilson. (The 2! comes from the relative order of Nancy and Wilson around Henry.)

So, the answer should be 9! - (2! * 8! + 2! * 8!) + 2! * 7!.

Note: Ignoring the last term gives your answer, but it just doesn't seem right to me to do that. Perhaps, someone can check what I wrote above...