'choose any three' is correct and usable in written English.
You can use it when you want to suggest a selection of items from a larger group of options. For example, "Please choose any three items from the menu."
These can be included in the appetizer bargain for two: choose any three openers for $14.
Choose any three of the Yankees' multitude of starters -- Mike Mussina, Contreras, David Wells Mussinaa, Contreras, Andy Pettitte; Roger Clemens, Mussina, Contreras; Wells, Pettitte, Contreras -- and they might not be as dominant as those three.
Choose any three of the above italicized reasons and show, step-by-step, how you would prove that these are the reasons why Giles believes in modern thought.
Choose any two 15-year-olds in South Africa; the odds say one of them will get AIDS.
Based on what an announcement on the Heat's Web site calls an "à la carte philosophy," fans can pick and choose any six games.
If Mr. Obama were to choose any two states in which to overperform, Ohio and Florida are pretty good picks, and both represent huge problems for Mr. Romney.
Mail-order beauty retailer Feel Unique has just launched its brilliant Pick'n'Mix scheme, allowing customers to choose any five generous beauty samples for free, no purchase necessary (you pay £3.95 p&p in exchange for a same-value gift voucher to redeem against future shopping).
The best time to visit Hortensia is at lunch, when a four-course prix fixe meal (4,750 yen, or about $58 at about 82 yen to the dollar) is offered; diners can choose any four dishes from the entire menu — even four entrees, say, or as one smartly dressed server earnestly suggested, four desserts.
Choose any two indices u and v∈{1,⋯,N} with u≠v.
We can choose any two different reduction ratios (H and L in Fig. 10) and design a gear clutch mechanism with the required HF travel range to suit the target application.
His point, presumably, is that in a given situation of choice, in which an agent has arrayed before himself a range of alternative natural goods that he has some reason to choose, he can choose any one of these goods, despite the advice given by reason.
