SQL SUM Across Tables

OK, I have to write a query to sum the values returned from multiple tables.  The details are as follows:

TABLE A contains the field I would like to sum, lets call it NUMBER in TABLE A.  TABLE B contains a set of classifications for records in TABLE A.  The field in TABLE B is CLASSIFICATION and can have the following values: CLASS 1, CLASS 2 and CLASS 3.  A single record in TABLE A can, and will, have many classifications in TABLE B.  For example, a single record in TABLE A can be CLASS 1, CLASS 2 and CLASS 3 and any combination thereof.  

I want to be able to sum the NUMBER field from TABLE A across records that have related records in TABLE B for CLASS 1, CLASS 2 and CLASS 3.  Please note in the example, the record in TABLE A must have all three classes to be valid for the summation.  If it only has CLASS 1 and CLASS 2, then it should not be included.

Assume a simplified data model as follows:

TABLE A
 - ID (unique identifier)
 - NUMBER

TABLE B
 - ID (relationship to TABLE A)
 - Classification