You see the secret of using Photoshop is in knowing when and how to use it's many different methods of making selections. The Quick Selection Tool is almost never the the right way to make decent and accurate selections. I used channels in this case because of the green color of the shamrock image. Bright green on a black background would be almost too easy!!!
I first opened the shamrock image and duplicated it using Cmd/Cntrl + J.
Turn off the original layer and select/highlight the duplicated layer.
Go to the channels panel and select the green channel layer. In the bottom of the channels panel there is a dotted circle Icon, click this to make a selection.
In the channels panel, click back on the RGB layer. Go back to your layers panel.
(note: Black and white is the goal when making selections with channels, in this case, the green channel leaves a perfect black and white example from which to make a selection)
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Note that the selection is of the green area and not the black. You must invert the selection with Shift + Cmd/Cntrl + I
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At this point you can either add a layer mask or you can delete the black background. You can also use the selection to create the layer mask for the second technique I describe above.
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Normally I never delete.....it's destructive. But since I made a duplicate layer of the original image layer, I'm not worried about deleting the BG in this case.......and it was (what I thought) easier to explain. It's hard to tell what people already know about Ps techniques.
Another excellent method for making a selection in this case would be in using Color Range.
