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(Historical note: In 2006-2007, the identical twin Kaczynski brothers were President and Prime Minister of Poland.)

## Normal straightforward solution:Case 0:If neither twin is elected, we have 8 * 7 * 6 * 5 = 1680 arrangements. Case 1:If one twin is elected, we have 4 positions for the twin * 8 * 7 * 6 ways to fill the other positions = 1344 arrangements. Case 2:If both twins are elected, we have 4C2 = 6 choices of positions for them * 8 * 7 = 6 * 56 = 336 arrangements. Total of all three cases: 3360. |
## More interesting solution:
Total, unrestricted arrangements = 10 * 9 * 8 * 7 = 5040.
For each of those, write the names of those elected
Suppose the twins are named Alice and Beth.
Since it doesn't matter which one comes first That leaves 3360 / 2 = 1680 for these cases.
The total then is 1680 "no twin" cases + 1680 "one or two twin" cases, |