Doughnuts

wolfram
Basically you start with 12 donuts, assign 3 of them to one person at random (220 ways)
Now you have 9 donuts, assign 3 of those to another person at random (84 ways)
Finally, you have 6 donuts, assign 3 of them to a third person at random (20 ways)
And the last person is stuck with whatever donuts are left (1 way)
Multiplying all of these together we get 220 * 84 * 20 * 1 = 369600

Answer
= 12! / (3!)⁴
= 369600

The first kid can have any 3 out of 12 doughnuts. Then the next kid can have any 3 from the remaining 9 doughnuts. The third kid can have any 3 from the 6 remaining doughnuts. The father gets the rest. This can be expressed as ${12 \choose 3 }\times{ 9\choose 3}\times {6\choose 3 }=\boxed{369600}$