I think that Zegroes answer is correct although I do not understand the explanation that he has given. 
The number of ways that 3 people can be chosen from 12 is 12C3 = 220
There are 9 people left. The number of ways that 4 people can be chosen from these is 9C4 = 126
There are 5 people left. The number of ways that 5 people can be chosen from these is 5C5 = 1
so the number of possible committees is 220 * 126 * 1 = 27720
you can choose in a different order if you wish but the answer will be the same. 