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

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SUMMARY

The discussion focuses on the correct method for subtracting all black hands in a specific problem identified as part (d). The user initially attempted to subtract 65,780 "all black" hands but realized that this approach was flawed because it did not account for the overlapping "all red" hands. The conclusion emphasizes the importance of considering all relevant categories when performing such calculations to avoid errors.

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Micky1964
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Can someone tell me where I'm going wrong here in part (d)?

Screen Shot 2021-09-25 at 8.01.10 pm.png

Answers from textbook:
Screen Shot 2021-09-25 at 8.01.28 pm.png

My attempt:
IMG_2935.JPG

Apologies for the blurry photo.
 
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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.
 

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