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Setting field values of a list item in SharePoint is easy.  But when it comes to Multi-Choice fields, the code is a big different.  The following code shows how values can be added to a multi-choice field.

SPFieldMultiChoice choiceField = (SPFieldMultiChoice)myWeb.Fields["choiceFieldName"];

choiceField.Choices.Add("Value");

//Set PushChangesToLists to true if automatic update of List or Content types is required

choiceField.PushChangesToLists = false; 

choiceField.Upate();