Nested IF with COUNTIF

I need to use a nested IF with COUNTIF.  Is that possible?  The scenario is that I need to count the number of “Red,” “Yellow,” and “Green” balls that are in a particular row in another sheet.  Then,

• If count of “Red”>=1, return “Red”
• If count of “Yellow”=1, return “Yellow”
• If count of “Green”=8 (or all), return “Green”

…in that hierarchy. 

I have the individual COUNTIF statements as follows:

=IF(COUNTIF({Copy of Compliance & Integration Detail Da Range 1}, "Red") >= 1, "Red") 

=IF(COUNTIF({Copy of Compliance & Integration Detail Da Range 1}, "Yellow") = 1, "Yellow") 

=IF(COUNTIF({Copy of Compliance & Integration Detail Da Range 1}, "Green") = 8, "Green")

Can't seem to figure out how to nest them into one IF statement with the embedded COUNTIF statements.