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# Counting with Symmetry - What's wrong with my solution?

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An international meeting is held between England, Germany, and France. Three representatives attend from England, four from Germany, and two from France. How many ways can all nine representatives sit around a circular table, if representatives of the same country sit together? (Two ways are considered the same if one can be rotated to produce the other.)

For each countries representatives, just choose the correct amount of consecutive seats: Thus there are 3! ways to place the representatives from England, 4! for Germany, and 2! for France. Thus the answer should be 3!*4!*2! = 288.

But this is wrong.

What did I s***w up on?

Jun 20, 2018

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If they sit around the table ....can they not be seated

3    2                          2      3

1              and             1            I don't think  these can be rotated to produce the other...so there would be   288 * 2   ways to be seated around the table.

Jun 20, 2018