MHB How Do I Correctly Subtract All Black Hands in Part (d)?

[Micky1964]

Can someone tell me where I'm going wrong here in part (d)?

Answers from textbook:

My attempt:

Apologies for the blurry photo.

 

[Micky1964]

Someone just pointed out to me my rather obvious mistake...When I subtract the 65780 "all black" hands, the rest of the hands will also still include the 65780 "all red" hands, so I should subtract those as well.
Funny how these things seem obvious in hindsight.