Permutation and Combination - Selections with Identical Objects

Paul was at the sushi section in a Japanese buffet, where there were \(3\) trays of sushi. The first tray had \(3\) pieces of unagi sushi, the second tray had \(2\) pieces of salmon sushi and the last tray had \(4\) pieces of ebi sushi. Find the number of ways in which Paul can choose at least one sushi from any of the trays.

TGM clarification: pieces of the same type of sushi are indistinguishable. A choice records the number taken of each type, with at least one piece in total.